YangQuan Chen

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer … Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.

Variable-order fractional differential operators in anomalous diffusion modeling

2009-07-22

HongGuang Sun , Wen Chen , YangQuan Chen

Matrix approach to discrete fractional calculus II: Partial fractional differential equations

2009-01-29

Igor Podlubný , Aleksei V. Chechkin , Tomáš Škovránek +2 more

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A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments

2009-07-01

HongSheng Li , Ying Luo , YangQuan Chen

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" … In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ¿ D ¿ controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative ( PD ¿ ) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.

A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

2011-03-01

HongGuang Sun , W. Chen , Hui Wei +1 more

On Riemann-Liouville and Caputo Derivatives

2011-01-01

Changpin Li , Deliang Qian , YangQuan Chen

Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important … Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann‐Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in science and engineering.

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Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

2004-12-01

YangQuan Chen , Blas M. Vinagre , Igor Podlubný

Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

2011-04-14

Changpin Li , Zhengang Zhao , YangQuan Chen

Fractional order [proportional derivative] controller for a class of fractional order systems

2009-07-31

Ying Luo , YangQuan Chen

Tuning fractional order proportional integral controllers for fractional order systems

2010-06-12

Ying Luo , YangQuan Chen , Chun Yang Wang +1 more

Fractional Calculus in Image Processing: A Review

2016-10-01

Qi Yang , Dali Chen , Tiebiao Zhao +1 more

A Modified Approximation Method of Fractional Order System

2006-06-01

Dingyü Xue , Chunna Zhao , YangQuan Chen

Many real world systems, including smart mechatronics systems, can be better characterized by dynamic systems of non-integer order. Using non-integer order or fractional order calculus, fractional order systems can be … Many real world systems, including smart mechatronics systems, can be better characterized by dynamic systems of non-integer order. Using non-integer order or fractional order calculus, fractional order systems can be modeled more authentically. Due to the nature of the infinite dimensional model, proper approximations to fractional order differentiator (s alpha , alpha isin Ropf) are fundamentally important. This paper contributed a new approximation scheme which is an extension of the well-established Oustaloup's approximation method. The benefits from using the proposed scheme are illustrated by numerical examples in both time and frequency domains

Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

2022-04-08

Estee Y. Cramer , Evan L Ray , Velma K. Lopez +7 more

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both … Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub ( https://covid19forecasthub.org/ ) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.

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Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

2012-07-12

Ying Luo , YangQuan Chen

Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality

2006-10-07

Hyo‐Sung Ahn , YangQuan Chen , Igor Podlubný

An approximate method for numerically solving fractional order optimal control problems of general form

2009-09-05

Christophe Tricaud , YangQuan Chen

UBIQUITOUS FRACTIONAL ORDER CONTROLS?

2006-01-01

YangQuan Chen

Distributed-Order Dynamic Systems

2012-01-01

YangQuan Chen , Igor Podlubný

A review and evaluation of numerical tools for fractional calculus and fractional order controls

2015-11-30

Zhuo Li , Lu Liu , Sina Dehghan +2 more

In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of … In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional integration/differentiation, and the simulation of fractional order systems. Time to time, being asked about which tool is suitable for a specific application, the authors decide to carry out this survey to present recapitulative information of the available tools in the literature, in hope of benefiting researchers with different academic backgrounds. With this motivation, the present article collects the scattered tools into a dashboard view, briefly introduces their usage and algorithms, evaluates the accuracy, compares the performance, and provides informative comments for selection.

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Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0<α<1 case

2017-04-04

Xuefeng Zhang , YangQuan Chen

Linear fractional order controllers; A survey in the frequency domain

2019-01-01

Ali Ahmadi Dastjerdi , Blas M. Vinagre , YangQuan Chen +1 more

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FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION

2012-03-14

HongGuang Sun , Wen Chen , Changpin Li +1 more

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the … Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable-order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank–Nicholson scheme are studied. Stability conditions for these three schemes are provided and proved via the Fourier method, rigorous convergence analysis is also performed. Two numerical examples are offered to verify the theoretical analysis of the above three schemes and illustrate the effectiveness of suggested schemes. The numerical results illustrate that, the implicit scheme and the Crank–Nicholson scheme can achieve high accuracy compared with the explicit scheme, and the Crank–Nicholson scheme claims highest accuracy in most situations. Moreover, some properties of variable-order time fractional diffusion equation model are also shown by numerical simulations.

Fractional differential models for anomalous diffusion

2010-03-09

HongGuang Sun , Wen Chen , Changpin Li +1 more

High-order algorithms for Riesz derivative and their applications (II)

2014-06-12

Hengfei Ding , Changpin Li , YangQuan Chen

Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole

2013-03-19

Hadi Malek , Ying Luo , YangQuan Chen

A Physical experimental study of variable-order fractional integrator and differentiator

2011-03-01

Hu Sheng , HongGuang Sun , Calvin Coopmans +2 more

Application of numerical inverse Laplace transform algorithms in fractional calculus

2010-12-17

Hu Sheng , Yan Li , YangQuan Chen

Experimental study of fractional order proportional derivative controller synthesis for fractional order systems

2010-11-24

Ying Luo , YangQuan Chen , Youguo Pi

High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)

2015-05-23

Jianxiong Cao , Changpin Li , YangQuan Chen

On mean square displacement behaviors of anomalous diffusions with variable and random orders

2009-12-17

HongGuang Sun , Wen Chen , Hu Sheng +1 more

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model

2020-08-01

Conghui Xu , Yongguang Yu , YangQuan Chen +1 more

In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a … In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number $${{ R }}_{0}$$ is derived. When $${{ R }}_{0}<1$$ , the disease-free equilibrium point is unique and locally asymptotically stable. When $${{ R }}_{0}>1$$ , the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

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Synthesis of multifractional Gaussian noises based on variable-order fractional operators

2011-01-26

Hu Sheng , HongGuang Sun , YangQuan Chen +1 more

FaultFace: Deep Convolutional Generative Adversarial Network (DCGAN) based Ball-Bearing failure detection method

2020-07-17

Jairo Viola , YangQuan Chen , Jing Wang

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The United States COVID-19 Forecast Hub dataset

2022-08-01

Estee Y. Cramer , Yuxin Huang , Yijin Wang +7 more

Abstract Academic researchers, government agencies, industry groups, and individuals have produced forecasts at an unprecedented scale during the COVID-19 pandemic. To leverage these forecasts, the United States Centers for Disease … Abstract Academic researchers, government agencies, industry groups, and individuals have produced forecasts at an unprecedented scale during the COVID-19 pandemic. To leverage these forecasts, the United States Centers for Disease Control and Prevention (CDC) partnered with an academic research lab at the University of Massachusetts Amherst to create the US COVID-19 Forecast Hub. Launched in April 2020, the Forecast Hub is a dataset with point and probabilistic forecasts of incident cases, incident hospitalizations, incident deaths, and cumulative deaths due to COVID-19 at county, state, and national, levels in the United States. Included forecasts represent a variety of modeling approaches, data sources, and assumptions regarding the spread of COVID-19. The goal of this dataset is to establish a standardized and comparable set of short-term forecasts from modeling teams. These data can be used to develop ensemble models, communicate forecasts to the public, create visualizations, compare models, and inform policies regarding COVID-19 mitigation. These open-source data are available via download from GitHub, through an online API, and through R packages.

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Fractional calculus and its applications

2013-04-02

Changpin Li , YangQuan Chen , Jürgen Kurths

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Random-order fractional differential equation models

2010-02-09

HongGuang Sun , YangQuan Chen , Wen Chen

Fractional order constitutive model of geomaterials under the condition of triaxial test

2012-10-15

D. Yin , Hao Wu , Chen Cheng +1 more

SUMMARY Fractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials; however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the topic of … SUMMARY Fractional calculus has been successfully applied to characterize the rheological property of viscoelastic materials; however, geomaterials were seldom involved in fractional order constitutive models (FOCM), and the topic of first loading and then unloading is rarely discussed through fractional calculus. In this paper, mechanical properties are considered as a ‘spectrum’, both ends of which are elasticity and viscosity, and the fractional order can be utilized to describe such properties quantitatively. In addition to conditions such as creep, stress‐relaxation, and constant‐strain‐rate loading, stress‐strain relationship under the condition of first loading and then unloading was also derived using FOCM. FOCM is then adopted to simulate triaxial tests of geomaterials under corresponding conditions. A comparison of test and numerical results demonstrates that FOCM can reasonably describe the mechanical characteristics of geomaterials.Copyright © 2012 John Wiley & Sons, Ltd.

Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders

2013-04-02

Igor Podlubný , Tomáš Škovránek , Blas M. Vinagre +3 more

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by … In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations.

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Regional Analysis of Time-Fractional Diffusion Processes

2018-01-01

Fudong Ge , YangQuan Chen , Chunhai Kou

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

2020-08-01

Zhenzhen Lu , Yongguang Yu , YangQuan Chen +4 more

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On the bound of the Lyapunov exponents for the fractional differential systems

2010-03-01

Changpin Li , Ziqing Gong , Deliang Qian +1 more

In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, … In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents. For linear fractional differential system, the bounds of its Lyapunov exponents are conveniently derived which can be regarded as an example for the theoretical results established in this paper. Numerical example is also included which supports the theoretical analysis.

Genetic Algorithm-Based Identification of Fractional-Order Systems

2013-05-06

Shengxi Zhou , Junyi Cao , YangQuan Chen

Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering … Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.

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Stability analysis of nonlinear Hadamard fractional differential system

2019-06-04

Guotao Wang , Ke Pei , YangQuan Chen

Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the US

2021-02-05

Estee Y. Cramer , Evan L Ray , Velma K. Lopez +7 more

Abstract Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and … Abstract Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub ( https://covid19forecasthub.org/ ) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multi-model ensemble forecast that combined predictions from dozens of different research groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-week horizon 3-5 times larger than when predicting at a 1-week horizon. This project underscores the role that collaboration and active coordination between governmental public health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks. Significance Statement This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the US. Results show high variation in accuracy between and within stand-alone models, and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public health action.

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On the existence of blow up solutions for a class of fractional differential equations

2014-09-02

Zhanbing Bai , YangQuan Chen , Hairong Lian +1 more

In this paper, by using fixed-point theorems, and lower and upper solution method, the existence for a class of fractional initial value problem (FIVP) $\begin{gathered} D_{0 + }^\alpha u(t) = … In this paper, by using fixed-point theorems, and lower and upper solution method, the existence for a class of fractional initial value problem (FIVP) $\begin{gathered} D_{0 + }^\alpha u(t) = f(t,u(t)),t \in (0,h), \hfill \\ t^{2 - \alpha } u(t)|_{t = 0} = b_1 D_{0 + }^{\alpha - 1} u(t) = |_{t = 0} = b_2 , \hfill \\ \end{gathered} $ is discussed, where f ∈ C([0, h]×R,R), D 0+ α u(t) is the standard Riemann-Liouville fractional derivative, 1 < α < 2. Some hidden confusion and fallacy in the literature are commented. A new condition on the nonlinear term is given to guarantee the equivalence between the solution of the FIVP and the fixed-point of the operator. Based on the new condition, some new existence results are obtained and presented as example.

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Asymptotical stability of fractional order systems with time delay via an integral inequality

2018-04-10

Bin‐Bin He , Hua‐Cheng Zhou , YangQuan Chen +1 more

In this study, the asymptotical stability for several classes of fractional order differential systems with time delay is investigated. The authors first present an integral inequality by which the Halanay … In this study, the asymptotical stability for several classes of fractional order differential systems with time delay is investigated. The authors first present an integral inequality by which the Halanay inequality is extended to fractional order case. Based on the generalised Halanay inequality, the authors establish several asymptotical stability conditions under which the fractional order systems with time delay are asymptotically stable. It is worth to note that these stability conditions are easy to check without resorting to the solution expression of the systems.

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Multi-robot area coverage and source localization method based on variational sparse Gaussian process

2025-05-21

Kai Cao , Yunbo Wei , YangQuan Chen +3 more

Abstract This paper introduces a distributed online learning coverage control algorithm based on sparse Gaussian process regression for addressing the problem of multi-robot area coverage and source localization in unknown … Abstract This paper introduces a distributed online learning coverage control algorithm based on sparse Gaussian process regression for addressing the problem of multi-robot area coverage and source localization in unknown environments. Considering the limitations of traditional Gaussian process regression in handling large datasets, this study employs multiple robots to explore the task area to gather environmental information and approximate the posterior distribution of the model using variational free energy methods, which serves as the input for the centroid Voronoi tessellation algorithm. Additionally, taking into consideration the localization errors, and the impact of obstacles, buffer factors and centroid Voronoi tessellation algorithms with separating hyperplanes are introduced for dynamic robot task area planning, ultimately achieving autonomous online decision-making and optimal coverage. Simulation results demonstrate that the proposed algorithm ensures the safety of multi-robot formations, exhibits higher iteration speed, and improves source localization accuracy, highlighting the effectiveness of model enhancements.

Changes in microbiome composition after fecal microbiota transplantation via oral gavage and magnetic navigation technology-assisted proximal colon/cecum enema in antibiotic knock-down rats: a comparative experimental study

2025-05-15

Xian-Jie Bai , Yu-Chen Mei , Jia-Tong Zhao +7 more

IL7-IL7R Interaction Mediates Fibroblast-Driven Macrophage-to-Osteoclast Differentiation in Periodontitis

2025-05-01

Pengjie Huang , Li Gao , Jiezhong Guan +7 more

To identify osteoclastogenic macrophage subsets and their regulatory mechanisms in periodontitis. We integrated single-cell RNA sequencing datasets from human and murine periodontitis to construct a comprehensive macrophage and monocyte atlas. … To identify osteoclastogenic macrophage subsets and their regulatory mechanisms in periodontitis. We integrated single-cell RNA sequencing datasets from human and murine periodontitis to construct a comprehensive macrophage and monocyte atlas. Employing functional enrichment, cell-cell communication, pseudotime, transcription factor, and machine learning analyses, we characterized and selected the specific macrophage subset involved in cell interactions. In vitro and in vivo experiments, including enzyme-linked immunosorbent assay, TRAP staining, micro-CT, qPCR, flow cytometry, and immunofluorescence staining, were performed to dissect the osteoclastogenic potential of specific macrophage subsets and to identify the key pathways. We discovered that the IL7R+ macrophage subset possesses significant osteoclast differentiation potential. Our findings indicate that the IL7/IL7R signaling axis facilitates osteoclast differentiation. Genes highly expressed in IL7R+ macrophages were identified as strong predictors for periodontitis by machine learning models. In vivo and in vitro experimental validation confirmed an increase in IL7R+ macrophages, along with their enhanced osteoclastogenic capacity. confirmed an increase in IL7R+ macrophages, along with their osteoclastogenic capacity. The inhibition of the IL7/IL7R signaling pathway was found to mitigate periodontitis progression by impeding osteoclast differentiation. Furthermore, fibroblasts were found to secret IL7 interacting with IL7 receptors on macrophages. Our study identifies IL7R+ macrophages as potential osteoclast precursors in periodontitis. We demonstrate that the IL7/IL7R signaling pathway is a critical driver of osteoclast differentiation. Moreover, targeting IL7R is a potential therapeutic strategy to curb periodontitis bone resorption.

Short-term wind power forecast with turning weather based on DBSCAN-RFE-LightGBM

2025-05-01

Donghai Li , Xinyu Fan , Gui‐Bin Bian +3 more

AEIA-MN: Evaluating the Robustness of Multimodal LLM-Powered Mobile Agents Against Active Environmental Injection Attacks

2025-02-18

YangQuan Chen , Xueyu Hu , Keting Yin +2 more

As researchers continuously optimize AI agents to perform tasks more effectively within operating systems, they often neglect to address the critical need for enabling these agents to identify "impostors" within … As researchers continuously optimize AI agents to perform tasks more effectively within operating systems, they often neglect to address the critical need for enabling these agents to identify "impostors" within the system. Through an analysis of the agents' operating environment, we identified a potential threat: attackers can disguise their attack methods as environmental elements, injecting active disturbances into the agents' execution process, thereby disrupting their decision-making. We define this type of attack as Active Environment Injection Attack (AEIA). Based on this, we propose AEIA-MN, an active environment injection attack scheme that exploits interaction vulnerabilities in the mobile operating system to evaluate the robustness of MLLM-based agents against such threats. Experimental results show that even advanced MLLMs are highly vulnerable to this attack, achieving a maximum attack success rate of 93% in the AndroidWorld benchmark.

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Stabilization of a Class of Fractional-Order Nonlinear Systems Subject to Actuator Saturation and Time Delay

2025-02-11

Esmat Sadat Alaviyan Shahri , Naser Pariz , YangQuan Chen

Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order … Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: the vector Lyapunov function method, integrated with the M-matrix approach, and the second one is the Lyapunov-like function method, which incorporates diffusive realization and the Lipchitz condition. An optimization framework is proposed to design stabilizing controllers based on the derived stability conditions. The proposed methods are validated numerically through their application to the FO Lorenz and Liu systems, demonstrating their effectiveness in handling actuator saturation and time delay.

Fractional-Order Singular Systems

2025-02-11

Qing‐Hao Zhang , Jun-Guo Lu , YangQuan Chen

This book explores robust control strategies to manage the inherent uncertainties and maintain the admissibility and performance of fractional-order singular systems. It covers essential topics such as system admissibility, robust … This book explores robust control strategies to manage the inherent uncertainties and maintain the admissibility and performance of fractional-order singular systems. It covers essential topics such as system admissibility, robust stabilization, H∞ control, positive real control, fault detection, delay systems, and provides a comprehensive framework for both the theoretical analysis and practical implementation of robust control methods.

ARMOR: Shielding Unlearnable Examples against Data Augmentation

2025-01-15

X Gong , Yuehang Wang , YangQuan Chen +6 more

Private data, when published online, may be collected by unauthorized parties to train deep neural networks (DNNs). To protect privacy, defensive noises can be added to original samples to degrade … Private data, when published online, may be collected by unauthorized parties to train deep neural networks (DNNs). To protect privacy, defensive noises can be added to original samples to degrade their learnability by DNNs. Recently, unlearnable examples are proposed to minimize the training loss such that the model learns almost nothing. However, raw data are often pre-processed before being used for training, which may restore the private information of protected data. In this paper, we reveal the data privacy violation induced by data augmentation, a commonly used data pre-processing technique to improve model generalization capability, which is the first of its kind as far as we are concerned. We demonstrate that data augmentation can significantly raise the accuracy of the model trained on unlearnable examples from 21.3% to 66.1%. To address this issue, we propose a defense framework, dubbed ARMOR, to protect data privacy from potential breaches of data augmentation. To overcome the difficulty of having no access to the model training process, we design a non-local module-assisted surrogate model that better captures the effect of data augmentation. In addition, we design a surrogate augmentation selection strategy that maximizes distribution alignment between augmented and non-augmented samples, to choose the optimal augmentation strategy for each class. We also use a dynamic step size adjustment algorithm to enhance the defensive noise generation process. Extensive experiments are conducted on 4 datasets and 5 data augmentation methods to verify the performance of ARMOR. Comparisons with 6 state-of-the-art defense methods have demonstrated that ARMOR can preserve the unlearnability of protected private data under data augmentation. ARMOR reduces the test accuracy of the model trained on augmented protected samples by as much as 60% more than baselines.

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SNC-Enabled Delay Analysis and DRL-based Power Control for RSMA Systems

2025-01-01

YangQuan Chen , Mengying Sun , Xiaodong Xu +5 more

A collection of correct fractional calculus for discontinuous functions

2024-12-02

Feng Tian , YangQuan Chen

DRiVE: Diffusion-based Rigging Empowers Generation of Versatile and Expressive Characters

2024-11-26

Mingze Sun , Junhao Chen , Junting Dong +7 more

Recent advances in generative models have enabled high-quality 3D character reconstruction from multi-modal. However, animating these generated characters remains a challenging task, especially for complex elements like garments and hair, … Recent advances in generative models have enabled high-quality 3D character reconstruction from multi-modal. However, animating these generated characters remains a challenging task, especially for complex elements like garments and hair, due to the lack of large-scale datasets and effective rigging methods. To address this gap, we curate AnimeRig, a large-scale dataset with detailed skeleton and skinning annotations. Building upon this, we propose DRiVE, a novel framework for generating and rigging 3D human characters with intricate structures. Unlike existing methods, DRiVE utilizes a 3D Gaussian representation, facilitating efficient animation and high-quality rendering. We further introduce GSDiff, a 3D Gaussian-based diffusion module that predicts joint positions as spatial distributions, overcoming the limitations of regression-based approaches. Extensive experiments demonstrate that DRiVE achieves precise rigging results, enabling realistic dynamics for clothing and hair, and surpassing previous methods in both quality and versatility. The code and dataset will be made public for academic use upon acceptance.

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Stability and l∞ Performance Analysis for Nabla Discrete Fractional Linear Positive System with Time-Varying Delays

2024-11-13

Cuihong Wang , Xueli Cui , Yanrong Cao +1 more

In this paper, the stability and l∞-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition … In this paper, the stability and l∞-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the system’s positivity. Then, based on the system’s positivity property, an asymptotically stable condition is established. Furthermore, it is demonstrated that the l∞-gain of such systems is determined by the system matrices and is independent of the magnitude of delays. Finally, numerical examples are provided to demonstrate the validity of the obtained results.

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SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation

2024-09-17

Mingze Sun , Guo Chen , Puhua Jiang +3 more

In this paper, we propose SRIF, a novel Semantic shape Registration framework based on diffusion-based Image morphing and Flow estimation. More concretely, given a pair of extrinsically aligned shapes, we … In this paper, we propose SRIF, a novel Semantic shape Registration framework based on diffusion-based Image morphing and Flow estimation. More concretely, given a pair of extrinsically aligned shapes, we first render them from multi-views, and then utilize an image interpolation framework based on diffusion models to generate sequences of intermediate images between them. The images are later fed into a dynamic 3D Gaussian splatting framework, with which we reconstruct and post-process for intermediate point clouds respecting the image morphing processing. In the end, tailored for the above, we propose a novel registration module to estimate continuous normalizing flow, which deforms source shape consistently towards the target, with intermediate point clouds as weak guidance. Our key insight is to leverage large vision models (LVMs) to associate shapes and therefore obtain much richer semantic information on the relationship between shapes than the ad-hoc feature extraction and alignment. As a consequence, SRIF achieves high-quality dense correspondences on challenging shape pairs, but also delivers smooth, semantically meaningful interpolation in between. Empirical evidence justifies the effectiveness and superiority of our method as well as specific design choices. The code is released at https://github.com/rqhuang88/SRIF.

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Event-triggered control for boundary controlled time-fractional diffusion systems with spatially-varying coefficients

2024-05-21

Fudong Ge , YangQuan Chen

Explicit stability condition for delta fractional order systems with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e385" altimg="si6.svg"><mml:mrow><mml:mi>α</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mo>+</mml:mo><mml:mi>∞</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

2024-05-01

Yiheng Wei , Shuaiyu Zhou , YangQuan Chen +1 more

A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler–Nichols approach

2024-05-01

Chuanfan Lu , R. Tang , Chuang Li +3 more

CO2 capture in a novel rotating spiral contactor with hydraulic seal: Hydromechanics, mass transfer and modeling

2024-02-17

YangQuan Chen , Meiqin Zheng , Chenghui Zheng +4 more

Fractional Order Euler-Lagrange Model for Accelerated Gradient Methods

2024-01-01

Osama F. Abdel Aal , Jairo Viola , YangQuan Chen

Optimal Control of Nonlinear Competitive Epidemic Spreading Processes With Memory in Heterogeneous Networks

2024-01-01

Jin You , Yan Li , Xiangyang Cao +3 more

Optimal control strategy for optimizing cancer cell growth model

2023-12-06

Hongyu Zhou , L. Liu , YangQuan Chen

Self-Similarity Principle and the General Theory of Fractal Elements: How to Fit a Random Curve with a Clearly Expressed Trend?

2023-06-20

Raoul R. Nigmatullin , YangQuan Chen

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with … The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but crucial adjustments. These new discoveries have the potential to significantly alter the preexisting theory and create new connections between it and its experimental support, particularly when it comes to measurements of the impedances of diverse metamaterials. It is now easy to demonstrate that any random curve with a clearly stated tendency in a specific range of scales is self-similar using the method involving reduction to three invariant points (Ymx, Ymn, and Ymin). This useful procedure indicates that the chosen random curve, even after being compressed a certain number of times, still resembles the original curve. Based on this common peculiarity, it is now possible to derive “a universal” fitting function that can be used in a variety of applied sciences, particularly those that deal with complex systems, to parametrize many initial curves when a model fitting function derived from a simple model is not present. This self-similarity principle-derived function demonstrates its effectiveness in data linked to photodiode noise and the smoothed integral curves produced from well-known transcendental numbers E and Pi, which are considered in the paper as an example.

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Asymptotic behavior of fractional-order nonlinear systems with two different derivatives

2023-05-15

Liping Chen , Min Xue , António M. Lopes +2 more

Abstract This paper addresses the asymptotic behavior of systems described by nonlinear differential equations with two fractional derivatives. Using the Mittag–Leffler function, the Laplace transform, and the generalized Gronwall inequality, … Abstract This paper addresses the asymptotic behavior of systems described by nonlinear differential equations with two fractional derivatives. Using the Mittag–Leffler function, the Laplace transform, and the generalized Gronwall inequality, a sufficient asymptotic stability condition is derived for such systems. Numerical examples illustrate the theoretical results.

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Fractional modeling and optimal control strategies for mutated COVID‐19 pandemic

2023-05-02

Weiyuan Ma , Nuri Ma , Changping Dai +2 more

As the COVID‐19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR‐type … As the COVID‐19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR‐type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID‐19 pandemic. The existence, uniqueness, boundedness, and nonnegativeness of the fractional model are derived. Based on the basic reproduction number , locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin's maximum principle, and the corresponding optimal solutions are derived for mitigation COVID‐19 transmission. The numerical results show that humans will coexist with COVID‐19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates.

Multiple models for outbreak decision support in the face of uncertainty

2023-04-25

Katriona Shea , Rebecca K. Borchering , William J. M. Probert +7 more

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. … Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.

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A multimodal hybrid stochastic-based deterministic ARFIMA model for the sustainable analysis of COVID-19 pandemic

2023-03-13

Ayaz Hussain Bukhari , Ejaz Ahmed , Muhammad Asif Zahoor Raja +2 more

The revise abstract is given as follows: The rapid emergence of the super-spreader COVID-19 with severe economic calamities with devastating social impact worldwide created the demand for effective research on … The revise abstract is given as follows: The rapid emergence of the super-spreader COVID-19 with severe economic calamities with devastating social impact worldwide created the demand for effective research on the spread dynamics of the disease to combat and create surveillance systems on a global scale. In this study, a novel hybrid Deterministic Autoregressive Fractional Integral Moving Average (ARFIMA) model is presented to forecast the bimodal COVID-19 transmission dynamics. The heterogeneity of multimodal behavior of the COVID-19 pandemic in Pakistan is modeled by a hybrid paradigm, in which a deterministic pattern is combined with the ARFIMA model to absorb the inherent chaotic pattern of the pandemic spread. The fractional fluctuation of the real epidemic system is effectively taken as a paradigm by stochastic type improved the deterministic model and ARFIMA process. Special transformations are also introduced to enhance the convergent rate of the bimodal paradigm in deterministic modeling. The outcome of the improved deterministic model is combined with the ARFIMA model is evaluated on the spread pattern of pandemic data in Pakistan for the next 30 days. The performance-indices of the hybrid-model based on Relative-Errors and RMSE statistics confirmed the effectiveness of the proposed paradigm for long-term epidemic modeling compared to other classical and machine learning algorithms.

Lyapunov Stability Analysis for Incommensurate Nabla Fractional Order Systems

2023-02-18

Yiheng Wei , Xuan Zhao , Yingdong Wei +1 more

Optimal regional control for a class of semilinear time-fractional diffusion systems with distributed feedback

2023-01-25

Fudong Ge , YangQuan Chen

A class of anomalous diffusion epidemic models based on CTRW and distributed delay

2022-12-24

Zhenzhen Lu , Guojian Ren , YangQuan Chen +2 more

In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast … In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast to the traditional reaction–diffusion epidemic models. The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable. Specifically, based on the continuous-time random walk (CTRW), starting from two stochastic processes of the waiting time and the step length, time-fractional space-fractional diffusion, time-fractional reaction–diffusion and fractional-order diffusion can all be naturally introduced into the SIR (S: susceptible, I: infectious and R: recovered) epidemic models, respectively. The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays. Distributed time delay systems can also be reduced to existing models, such as the standard SIR model, the fractional infectivity model and others, within the proper bounds. Meanwhile, as an application of the above stochastic modeling method, the physical meaning of anomalous diffusion is also considered by taking the SEIR (E: exposed) epidemic model as an example. Similar methods can be used to build other types of epidemic models, including SIVRS (V: vaccine), SIQRS (Q: quarantined) and others. Finally, this paper describes the transmission of infectious disease in space using the real data of COVID-19.

The effect mitigation measures for COVID-19 by a fractional-order SEIHRDP model with individuals migration

2022-12-14

Zhenzhen Lu , YangQuan Chen , Yongguang Yu +4 more

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Lyapunov stability analysis for nonlinear nabla tempered fractional order systems

2022-12-04

Yiheng Wei , YangQuan Chen , Yingdong Wei +1 more

Abstract Due to the restriction of practical systems in time or space, tempered fractional calculus becomes more reasonable than the traditional fractional calculus. It is known that stability analysis is … Abstract Due to the restriction of practical systems in time or space, tempered fractional calculus becomes more reasonable than the traditional fractional calculus. It is known that stability analysis is a crucial issue for control systems. This paper concerns the stability analysis issue of nabla tempered fractional order systems for the first time. The (discrete time) tempered Mittag–Leffler stability is defined firstly and then a stability criterion is derived via Lyapunov method. Besides, boundedness and attractiveness are also investigated.

Robust tilt‐integral‐derivative controller synthesis for first‐order plus time delay and higher‐order systems

2022-11-21

Chuanfan Lu , Rongnian Tang , YangQuan Chen +1 more

ABSTRACT A tilt integrator of the tilt‐integral‐derivative (TID) controller is an integrator to the power of a fraction. The current state of the art of TID controller is difficult to … ABSTRACT A tilt integrator of the tilt‐integral‐derivative (TID) controller is an integrator to the power of a fraction. The current state of the art of TID controller is difficult to satisfy prespecified frequency‐domain specifications and is not able to build the connection between the frequency‐domain synthesis and time‐domain analysis. To fill the gap in TID control theory, a systematic tuning method of robust TID controller for first order plus time delay (FOPTD) and higher‐order processes is proposed, which is based on combining frequency‐ and time‐domain specifications synthesis. The TID controller parameters , , and optimal fractional order are settled to meet frequency‐domain specifications including phase margin, gain crossover frequency, and flat phase constraint that guarantee systemic stability and robustness. The parameter can be determined under the time‐domain specification including the smallest ITAE that achieves optimal dynamic performance. In addition, the steps of the proposed robust TID controller design process are given in detail, and an example is given to illustrate the corresponding steps. At last, the control and gain variation performances of the obtained TID controller are compared with some other controllers (PID, FOPI, and FOPID). Simulation results for FOPTD and higher‐order systems illustrate the superior robustness as well as the transient performance of the proposed control tuning procedure. To verify the practical usefulness of the outcomes of this paper, some experimental results on temperature control of a Peltier cell are presented.

Fractional modelling and optimal control strategies for mutated COVID-19 pandemic

2022-10-24

Weiyuan Ma , Nuri Ma , Changping Dai +2 more

As the COVID-19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR-type … As the COVID-19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR-type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID-19 pandemic. The existence, uniqueness, boundedness and nonnegativeness of the fractional model are derived. Based on the basic reproduction number R 0 , locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the R 0 and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin’s Maximum Principle, and the corresponding optimal solutions are derived for mitigation COVID-19 transmission. The numerical results show that humans will coexist with COVID-19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates.

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The United States COVID-19 Forecast Hub dataset

2022-08-01

Estee Y. Cramer , Yuxin Huang , Yijin Wang +7 more

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Stability and Stabilization of Fractional-Order Uncertain Nonlinear Systems With Multiorder

2022-05-26

Liping Chen , Wenliang Guo , Panpan Gu +3 more

Fractional-order (FO) commensurate systems have been widely studied in recent years, including their stability and control. However, for incommensurate FO systems these problems are still challenging and further research is … Fractional-order (FO) commensurate systems have been widely studied in recent years, including their stability and control. However, for incommensurate FO systems these problems are still challenging and further research is needed. In this brief, the stability and stabilization of incommensurate FO nonlinear systems with time-varying bounded uncertainties are investigated. A new stability criterion in the form of linear matrix inequality is formulated by employing the FO comparison principle of multi-order FO systems. Then, a state feedback controller for system stabilization is derived based on the stability criteria proposed. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

2022-05-23

Manashita Borah , Antara Gayan , Jiv Siddhi Sharma +3 more

Lyapunov stability criteria in terms of class <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e342" altimg="si5.svg"><mml:mi mathvariant="script">K</mml:mi></mml:math> functions for Riemann–Liouville nabla fractional order systems

2022-05-17

Yiheng Wei , Xuan Zhao , Yingdong Wei +1 more

Robust three‐parameter fractional‐order proportional integral derivative controller synthesis for permanent magnet synchronous motor speed servo system

2022-05-10

Pengchong Chen , Weijia Zheng , Ying Luo +2 more

Abstract This paper proposes a three‐parameter fractional‐order PID (TPFOPID) controller synthesis for the PMSM speed servo system. This TPFOPID contains complete proportional/integral/differential elements but with only three parameters to tune. … Abstract This paper proposes a three‐parameter fractional‐order PID (TPFOPID) controller synthesis for the PMSM speed servo system. This TPFOPID contains complete proportional/integral/differential elements but with only three parameters to tune. A systematic design scheme of this TPFOPID to satisfy a flat phase constraint and two specifications, that is, gain crossover frequency ( ) and phase margin ( ), is presented for the PMSM speed servo system. Furthermore, the entire achievable region of and can be collected following the scheme. With this region, one can choose feasible combination specifications of and before the controller design. To show the effectiveness of the TPFOPID controller, the achievable region of specifications is compared with the fractional‐order PI (FOPI) also with three parameters. Simulation illustration and experimental verifications using the TPFOPID for the PMSM speed servo system are presented and compared with those using FOPI controller, IOPI controller, and IOPID controller to demonstrate the advantages of the designed TPFOPID controller, and also compared with FOPID based on differential evolution (DE) algorithm to present comparable control performance.

Stability Analysis of the Nabla Distributed-Order Nonlinear Systems

2022-04-20

Cuihong Wang , Tianfen Zhu , YangQuan Chen

The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems … The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on Lyapunov direct method. In addition, some properties of the nabla distributed-order operators are derived. Based on these properties, a simpler criterion is provided to determine the stability of such systems. Finally, two examples are given to illustrate the validity of these results.

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Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

2022-04-08

Estee Y. Cramer , Evan L Ray , Velma K. Lopez +7 more

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How to empower Grünwald–Letnikov fractional difference equations with available initial condition?

2022-04-05

Yiheng Wei , Jinde Cao , Chuang Li +1 more

In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)), k > … In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)), k > a + 1, cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp.

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Stability analysis of a nonlocal SIHRDP epidemic model with memory effects

2022-02-23

Zhenzhen Lu , Yongguang Yu , YangQuan Chen +3 more

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Qualitative and quantitative analysis of the COVID-19 pandemic by a two-side fractional-order compartmental model

2022-01-12

Weiyuan Ma , Yanting Zhao , Lihong Guo +1 more

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Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022-01-01

Hua‐Cheng Zhou , Ze‐Hao Wu , Bao‐Zhu Guo +1 more

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external … In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in Liang [ Nonlinear Dyn. 38 (2004) 339–354] where all results were verified by simulations only.

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Fractional Order Random Sample Consensus

2022-01-01

Guoxiang Zhang , YangQuan Chen

Estimation via Mobile Sensors for Semilinear Time-Fractional Diffusion Processes

2021-12-22

Fudong Ge , YangQuan Chen

The purpose of this letter is to solve an extended observer design problem for state estimation of the anomalous sub-diffusion processes modeled by the 1D semilinear time-fractional diffusion systems. Toward … The purpose of this letter is to solve an extended observer design problem for state estimation of the anomalous sub-diffusion processes modeled by the 1D semilinear time-fractional diffusion systems. Toward this aim we introduce the mobile zone sensors, which are guided within a limited spatial support but can move throughout the spatial domain hence improving the estimation performance. An extended Luenberger-type observer that contains a state estimator and the guidance of mobile sensors is then designed to meet the desired design requirements. Finally, we finish with a numerical example to illustrate the effectiveness of our proposed method.

Solution Analysis and Novel Admissibility Conditions of SFOSs: The 1 < α < 2 Case

2021-10-02

Qing‐Hao Zhang , Jun‐Guo Lu , Jie Xu +1 more

This article considers the regularity, nonimpulsiveness, stability, as well as admissibility of singular fractional-order systems (SFOSs) with the fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (1,2)$ </tex-math></inline-formula> . First, the … This article considers the regularity, nonimpulsiveness, stability, as well as admissibility of singular fractional-order systems (SFOSs) with the fractional-order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in (1,2)$ </tex-math></inline-formula> . First, the existence and uniqueness of time-domain solutions of the systems are analyzed by using the Kronecker equivalent standard form, and then the necessary and sufficient condition for the regularity is proposed. Second, the explicit time-domain solutions of the systems are presented, which are the basis of the necessary and sufficient conditions for the nonimpulsiveness and stability. Third, two novel necessary and sufficient conditions for the admissibility of the systems are proposed in terms of the nonstrict linear matrix inequalities (LMIs) and strict LMIs, respectively. Finally, two numerical examples about the SFOSs are provided to illustrate the validity of the obtained conclusions.

A Metric For Evaluating 3d Reconstruction And Mapping Performance With No Ground Truthing

2021-08-23

Guoxiang Zhang , YangQuan Chen

It is not easy when evaluating 3D mapping performance because existing metrics require ground truth data that can only be collected with special instruments. In this paper, we propose a … It is not easy when evaluating 3D mapping performance because existing metrics require ground truth data that can only be collected with special instruments. In this paper, we propose a metric, dense map posterior (DMP), for this evaluation. It can work without any ground truth data. Instead, it calculates a comparable value, reflecting a map posterior probability, from dense point cloud observations. In our experiments, the proposed DMP is benchmarked against ground truth-based metrics. Results show that DMP can provide a similar evaluation capability. The proposed metric makes evaluating different methods more flexible and opens many new possibilities, such as self-supervised methods and more available datasets.

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Self-Optimizing Loop Sifting and Majorization for 3D Reconstruction

2021-08-17

Guoxiang Zhang , YangQuan Chen

Abstract Visual simultaneous localization and mapping (vSLAM) and 3D reconstruction methods have gone through impressive progress. These methods are very promising for autonomous vehicle and consumer robot applications because they … Abstract Visual simultaneous localization and mapping (vSLAM) and 3D reconstruction methods have gone through impressive progress. These methods are very promising for autonomous vehicle and consumer robot applications because they can map large-scale environments such as cities and indoor environments without the need for much human effort. However, when it comes to loop detection and optimization, there is still room for improvement. vSLAM systems tend to add the loops very conservatively to reduce the severe influence of the false loops. These conservative checks usually lead to correct loops rejected, thus decrease performance. In this paper, an algorithm that can sift and majorize loop detections is proposed. Our proposed algorithm can compare the usefulness and effectiveness of different loops with the dense map posterior (DMP) metric. The algorithm tests and decides the acceptance of each loop without a single user-defined threshold. Thus it is adaptive to different data conditions. The proposed method is general and agnostic to sensor type (as long as depth or LiDAR reading presents), loop detection, and optimization methods. Neither does it require a specific type of SLAM system. Thus it has great potential to be applied to various application scenarios. Experiments are conducted on public datasets. Results show that the proposed method outperforms state-of-the-art methods.

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A Fractional-Order Age-Structured Generalized SEIR Model: The Role of “COVID-19 Symptom Data Challenge” Dataset

2021-07-05

Yanting Zhao , Lihong Guo , Yong Wang +1 more

Prediction and Control of the Impact of the Onset Influenza Season on the Spread of COVID-19

2021-07-05

Lihong Guo , Yanting Zhao , YangQuan Chen

Coauthor	Papers Together
Fudong Ge	40
Chunhai Kou	28
Igor Podlubný	19
Yan Li	16
Changpin Li	15
Yongguang Yu	13
Yiheng Wei	13
Hu Sheng	12
Jairo Viola	12
Dingyü Xue	12
Juan Chen	11
Blas M. Vinagre	11
Ying Luo	11
Lihong Guo	11
Kevin L. Moore	10
Guoxiang Zhang	9
HongGuang Sun	9
Yanting Zhao	9
Kecai Cao	9
Yisheng Zhong	9
Caibin Zeng	8
Conghui Xu	8
Guojian Ren	8
Yuquan Chen	8
Jie Yuan	7
Lili Ma	7
Bo Zhuang	7
Sina Dehghan	7
Wen Chen	6
Tiebiao Zhao	6
Yang Zhao	6
Yong Wang	6
Hua‐Cheng Zhou	6
Baotong Cui	6
Abdullah Ateş	6
Jinsong Liang	6
Pan Xu	5
Xuefeng Zhang	5
Michael A. Johansson	5
Kunpeng Mu	5
Jinghui Chen	5
T. Alex Perkins	5
Yingdong Wei	5
Quanquan Gu	5
Tianshuang Qiu	5
Matthew Biggerstaff	5
Alessandro Vespignani	5
Geoffrey Fairchild	5
Guido España	5
Rachel J. Oidtman	5

Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers

1999-01-01

Igor Podlubný

Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The … Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.

Theory and Applications of Fractional Differential Equations

2006-01-01

Anatoly A. Kilbas , H. M. Srivastava , Juan J. Trujillo

Mittag–Leffler stability of fractional order nonlinear dynamic systems

2009-05-14

Yan Li , YangQuan Chen , Igor Podlubný

The random walk's guide to anomalous diffusion: a fractional dynamics approach

2000-12-01

Ralf Metzler , J. Klafter

Stability results for fractional differential equations with applications to control processing

1996-01-01

Denis Matignon

In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external … In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external stabilities are investigated. For fractional differential systems in polynomial representation, external stability is thoroughly examined. Our main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector |arg(σ)| ≤ απ/2, thus generalizing in a stupendous way the well-known results for the integer case α = 1.

Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability

2009-08-29

Yan Li , YangQuan Chen , Igor Podlubný

Lyapunov functions for fractional order systems

2014-02-03

Norelys Aguila‐Camacho , Manuel A. Duarte‐Mermoud , Javier A. Gallegos

On the Appearance of the Fractional Derivative in the Behavior of Real Materials

1984-06-01

Peter J. Torvik , Ronald L. Bagley

Generalized constitutive relationships for viscoelastic materials are suggested in which the customary time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification for … Generalized constitutive relationships for viscoelastic materials are suggested in which the customary time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification for such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the fractional derivative is shown to arise naturally in the description of certain motions of a Newtonian fluid. We claim this provides some justification for the use of ad hoc relationships which include the fractional derivative. An application of such a constitutive relationship to the prediction of the transient response of a frequency-dependent material is included.

Cyber-physical systems as general distributed parameter systems: three types of fractional order models and emerging research opportunities

2015-10-10

Fudong Ge , YangQuan Chen , Chunhai Kou

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three … Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

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Variable-order fractional differential operators in anomalous diffusion modeling

2009-07-22

HongGuang Sun , Wen Chen , YangQuan Chen

Fractional Calculus in Bioengineering

2007-02-12

Bruce J. West

Regional Analysis of Time-Fractional Diffusion Processes

2018-01-01

Fudong Ge , YangQuan Chen , Chunhai Kou

Actuator characterisations to achieve approximate controllability for a class of fractional sub-diffusion equations

2016-03-10

Fudong Ge , YangQuan Chen , Chunhai Kou

This paper is devoted to analysing the actuator characterisations for the fractional sub-diffusion equation under consideration to become approximately controllable. Two different cases are considered, where the control inputs emerge … This paper is devoted to analysing the actuator characterisations for the fractional sub-diffusion equation under consideration to become approximately controllable. Two different cases are considered, where the control inputs emerge in the differential equation as distributed inputs and as boundary inputs in the boundary conditions. The dual system for fractional sub-diffusion equation is solved and the necessary and sufficient conditions for the approximate controllability of the system are established. Several examples are worked out in the end to illustrate our results.

Boundary feedback stabilisation for the time fractional‐order anomalous diffusion system

2016-03-16

Fudong Ge , YangQuan Chen , Chunhai Kou

In this study, the authors attempt to explore the boundary feedback stabilisation for an unstable heat process described by fractional‐order partial differential equation (PDE), where the first‐order time derivative of … In this study, the authors attempt to explore the boundary feedback stabilisation for an unstable heat process described by fractional‐order partial differential equation (PDE), where the first‐order time derivative of normal reaction–diffusion equation is replaced by a Caputo time fractional derivative of order α∈(0, 1]. By designing an invertible coordinate transformation, the system under consideration is converted into a Mittag–Leffler stability linear system and the boundary stabilisation problem is transformed into a problem of solving a linear hyperbolic PDE. It is worth mentioning that with the help of this invertible coordinate transformation, they can explicitly obtain the closed‐loop solutions of the original problem. The output feedback problem with both anti‐collocated and collocated actuator/sensor pairs in one‐dimensional domain is also presented. A numerical example is given to test the effectiveness of the authors' results.

Tuning and auto-tuning of fractional order controllers for industry applications

2008-01-10

Concepción A. Monje , Blas M. Vinagre , V. Feliú +1 more

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Applications of Fractional Calculus in Physics

2000-01-01

R. Hilfer

An introduction to fractional calculus, P.L. Butzer & U. Westphal fractional time evolution, R. Hilfer fractional powers of infinitesimal generators of semigroups, U. Westphal fractional differences, derivatives and fractal time … An introduction to fractional calculus, P.L. Butzer & U. Westphal fractional time evolution, R. Hilfer fractional powers of infinitesimal generators of semigroups, U. Westphal fractional differences, derivatives and fractal time series, B.J. West and P. Grigolini fractional kinetics of Hamiltonian chaotic systems, G.M. Zaslavsky polymer science applications of path integration, integral equations, and fractional calculus, J.F. Douglas applications to problems in polymer physics and rheology, H. Schiessel et al applications of fractional calculus and regular variation in thermodynamics, R. Hilfer.

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

2011-04-30

Kenichi Sakamoto , Masahiro Yamamoto

Advances in Fractional Calculus

2007-01-01

Jocelyn Sabatier , Om P. Agrawal , J. A. Tenreiro Machado

A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments

2009-07-01

HongSheng Li , Ying Luo , YangQuan Chen

Regional controllability analysis of fractional diffusion equations with Riemann–Liouville time fractional derivatives

2016-12-09

Fudong Ge , YangQuan Chen , Chunhai Kou

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Boundary Feedback Stabilization for an Unstable Time Fractional Reaction Diffusion Equation

2018-01-01

Hua‐Cheng Zhou , Bao‐Zhu Guo

In this paper, we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations. New state feedback controls with actuation on one end are designed by the backstepping method … In this paper, we consider boundary feedback stabilization for unstable time fractional reaction diffusion equations. New state feedback controls with actuation on one end are designed by the backstepping method for both Dirichlet and Neumann boundary controls. By the Riesz basis approach and the fractional Lyapunov method, we prove the existence and uniqueness and the Mittag--Leffler stability for the closed-loop systems. For both cases, the observers and the observer-based output feedback are designed to stabilize the systems.

Closed-Form Boundary State Feedbacks for a Class of 1-D Partial Integro-Differential Equations

2004-12-01

Andrey Smyshlyaev , Miroslav Krstić

In this paper, a problem of boundary stabilization of a class of linear parabolic partial integro-differential equations (P(I)DEs) in one dimension is considered using the method of backstepping, avoiding spatial … In this paper, a problem of boundary stabilization of a class of linear parabolic partial integro-differential equations (P(I)DEs) in one dimension is considered using the method of backstepping, avoiding spatial discretization required in previous efforts. The problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic P(I)DE. The kernel P(I)DE is then converted into an equivalent integral equation and by applying the method of successive approximations, the equation's well posedness and the kernel's smoothness are established. It is shown how to extend this approach to design optimally stabilizing controllers. An adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller, and the performance bounds are derived. For a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed-loop solutions are found in closed form. A numerical scheme for the kernel P(I)DE is proposed; its numerical effort compares favorably with that associated with operator Riccati equations.

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Completely monotonic functions

2001-12-01

Kenneth S. Miller , Stefan Samko

In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. … In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function w is the Laplace transform of an infinitely divisible probability distribution on (0,∞), if and only if w = e-h , where the derivative of h is completely monotonic and h(0+) = 0.

Mittag-Leffler Functions, Related Topics and Applications

2014-01-01

Rudolf Gorenflo , Anatoly A. Kilbas , Francesco Mainardi +1 more

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Advances in fractional calculus: theoretical developments and applications in physics and Engineering

2007-06-01

Jocelyn Sabatier , Om P. Agrawal , J. A. Tenreiro Machado

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal … In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

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A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity

1983-06-01

Ronald L. Bagley , Peter J. Torvik

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite … Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation R. L. Bagley, P. J. Torvik; A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity. J. Rheol. 1 June 1983; 27 (3): 201–210. https://doi.org/10.1122/1.549724 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentThe Society of RheologyJournal of Rheology Search Advanced Search |Citation Search

Fractional order [proportional derivative] controller for a class of fractional order systems

2009-07-31

Ying Luo , YangQuan Chen

Existence of mild solutions for fractional neutral evolution equations

2009-07-16

Yong Zhou , Feng Jiao

LMI stability conditions for fractional order systems

2009-09-24

Jocelyn Sabatier , Mathieu Moze , Christophe Farges

Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model

2020-08-01

Conghui Xu , Yongguang Yu , YangQuan Chen +1 more

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Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

2006-05-24

XU Ming-yu , Wenchang Tan

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical … From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern mechanics. Some authors' researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

Remarks on fractional derivatives

2006-10-12

Changpin Li , Weihua Deng

Regional gradient controllability of sub-diffusion processes

2016-04-02

Fudong Ge , YangQuan Chen , Chunhai Kou

Mittag-Leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters

2018-11-16

Fudong Ge , Thomas Meurer , YangQuan Chen

Unbounded Control and Observation Systems and Their Duality

1978-07-01

A. J. Pritchard , Andrew Wirth

The paper considers some questions arising from a general theory of observation and control by Russell and Dolecki. For a distributed parameter system the observation may be restricted to the … The paper considers some questions arising from a general theory of observation and control by Russell and Dolecki. For a distributed parameter system the observation may be restricted to the boundary or some other subset, so the observation operator may be unbounded. If this operator satisfies certain conditions the dual control system operator can be defined. If also there is an appropriate Green's formula, the dual system is interpreted as one of control on a subset. For systems associated with biorthogonal sequences it is shown that the attainable sets cannot be fully characterized in terms of the sequence unless it is basic.

State-space representation for fractional order controllers

2000-07-01

H.‐F. Raynaud , A. Zergaı̈noh

Fractional calculus application in control systems

2002-12-04

Michael Axtell , M.E. Bise

Standard control systems can be characterized by type in the s-domain; typically these types are of integer order. Some of the implications of noninteger order systems in the s-domain are … Standard control systems can be characterized by type in the s-domain; typically these types are of integer order. Some of the implications of noninteger order systems in the s-domain are explored. To accomplish this, results from the area of fractional calculus, which defines mathematics of noninteger order derivative and integration, are utilized. Fractional calculus operators, Laplace transformed differintegrals are shown to behave differently from their standard integer-order counterparts.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

Discretized Fractional Calculus

1986-05-01

Ch. Lubich

For the numerical approximation of fractional integrals $I^\alpha f(x) = \frac{1}{{\Gamma (\alpha )}}\int_0^x {(x - s)^{\alpha - 1} f(s)ds\qquad (x \geqq 0)} $ with $f(x) = x^{\beta - 1} g(x)$, … For the numerical approximation of fractional integrals $I^\alpha f(x) = \frac{1}{{\Gamma (\alpha )}}\int_0^x {(x - s)^{\alpha - 1} f(s)ds\qquad (x \geqq 0)} $ with $f(x) = x^{\beta - 1} g(x)$, g smooth, we study convolution quadratures. Here approximations to $I^\alpha f(x)$ on the grid $x = 0,h,2h, \cdots ,Nh$ are obtained from a discrete convolution with the values of f on the same grid. With the appropriate definitions, it is shown that such a method is convergent of order p if and only if it is stable and consistent of order p. We introduce fractional linear multistep methods: The $\alpha $th power of a pth order linear multistep method gives a pth order convolution quadrature for the approximation of $I^\alpha $. The paper closes with numerical examples and applications to Abel integral equations, to diffusion problems and to the computation of special functions.

Random Walks on Lattices. II

1965-02-01

Elliott W. Montroll , George H. Weiss

Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice … Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points. The number of distinct points visited after n steps on a k-dimensional lattice (with k ≥ 3) when n is large is a1n + a2n½ + a3 + a4n−½ + …. The constants a1 − a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 are given for simple and face-centered cubic lattices. Formulas have also been obtained for the number of points visited r times in n steps as well as the average number of times a given point has been visited. The probability F(c) that a walker on a one-dimensional lattice returns to his starting point before being trapped on a lattice of trap concentration c is F(c) = 1 + [c/(1 − c)] log c. Most of the results in this paper have been derived by the method of Green's functions.

Fractional order state equations for the control of viscoelasticallydamped structures

1991-03-01

Ronald L. Bagley , R. CALICO

Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures. The mechanical properties of damping materials are modeled using fractional order … Fractional order state equations are developed to predict the effects of feedback intended to reduce motion in damped structures. The mechanical properties of damping materials are modeled using fractional order time derivatives of stress and strain. These models accurately describe the broadband effects of material damping in the structure's equations of motion. The resulting structural equations of motion are used to derive the fractional order state equations. Substantial differences between the structural and state equations are seen to exist. The mathematical form of the state equations suggests the feedback of fractional order time derivatives of structural displacements to improve control system performance. Several other advantages of the fractional order state formulation are discussed. Nomenclature

Fractional Differential Equations - An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications

1999-01-01

Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives

2005-11-28

Nicole Heymans , Igor Podlubný

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Mean fractional-order-derivatives differential equations and filters

1995-01-01

Michèle Caputo

Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality

2006-10-07

Hyo‐Sung Ahn , YangQuan Chen , Igor Podlubný

Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

2004-12-01

YangQuan Chen , Blas M. Vinagre , Igor Podlubný

On the Regional Controllability of the Sub-Diffusion Process with Caputo Fractional Derivative

2016-10-01

Fudong Ge , YangQuan Chen , Chunhai Kou +1 more

Optimal random search, fractional dynamics and fractional calculus

2014-03-20

Caibin Zeng , YangQuan Chen

What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Lévy flight is the best option … What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the Lévy flight is the best option to characterize this optimal problem, however, which ignores the understanding and learning abilities of the searcher agents. In this paper we propose the Continuous Time Random Walk (CTRW) optimal search framework and find the optimum for both of search length’s and waiting time’s distributions. Based on fractional calculus technique, we further derive its master equation to show the mechanism of such complex fractional dynamics. Numerous simulations are provided to illustrate the non-destructive and destructive cases.

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UBIQUITOUS FRACTIONAL ORDER CONTROLS?

2006-01-01

YangQuan Chen

Probability distributions generated by fractional diffusion equations

2007-01-01

Francesco Mainardi , Paolo Paradisi , Rudolf Gorenflo

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The … Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of these equations provide probability density functions, evolving on time or variable in space, which are related to the class of stable distributions. This property is a noteworthy generalization of what happens for the standard diffusion equation and can be relevant in treating financial and economical problems where the stable probability distributions play a key role.

Analytical impulse response of a fractional second order filter and its impulse response invariant discretization

2010-02-02

Yan Li , Hu Sheng , YangQuan Chen