Variable-order fractional differential operators in anomalous diffusion modeling

HongGuang Sun, Wen Chen, YangQuan Chen

Type: Article

Publication Date: 2009-07-22

Citations: 517

DOI: https://doi.org/10.1016/j.physa.2009.07.024

View Publication

Locations

Physica A Statistical Mechanics and its Applications - View

Similar Works

Action	Title	Year	Authors
+	Fractional differential models for anomalous diffusion	2010	HongGuang Sun Wen Chen Changpin Li YangQuan Chen
+	Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models	2016	Song Wei Wen Chen Y.C. Hon
+	Fractional model equation for anomalous diffusion	1994	Ralf Metzler Walter Glöckle Theo F. Nonnenmacher
+	Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver	2019	Xiaoting Liu HongGuang Sun Yong Zhang Chunmiao Zheng Zhongbo Yu
+	Anomalous fractional diffusion equation for transport phenomena	1999	Qiuhua Zeng Houqiang Li De Liu
+	Applications of Anomalous Transport and Fractional Modeling	2024
+	The meshless approach for solving 2D variable-order time-fractional advection–diffusion equation arising in anomalous transport	2021	Vahid Reza Hosseini Masoumeh Koushki Wennan Zou
+	Fractional diffusion equations and anomalous diffusion	2018	Muhammad Zubair
+	Fractional diffusion models of anomalous diffusion	2003	D. del-Castillo-Negrete B. A. Carreras V. E. Lynch
+	Variational Interpolation Method in Inverse Problems of Anomalous Diffusion of Fractional-Differential Type	2021	V. A. Litvinov V. V. Uchaikin
+	A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model	2020	Muhammad Hamid Muhammad Usman Rizwan Ul Haq W. Wang
+	Fractional nonlinear diffusion equation, solutions and anomalous diffusion	2006	A.T. Silva E. K. Lenzi L. R. Evangelista Marcelo Kaminski Lenzi L. R. da Silva
+	Anomalous diffusion expressed through fractional order differential operators in the Bloch–Torrey equation	2007	Richard L. Magin Osama Abdullah Dumitru Băleanu Xiaohong Joe Zhou
+	Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison	2018	Xiangnan Yu Yong Zhang HongGuang Sun Chunmiao Zheng
+	Fractional Diffusion Model, Anomalous Statistics and Random Process	2022	Wen Chen HongGuang Sun Xicheng Li
+	Fractional Calculus and Applications to Fractional Oscillation and Anomalous Diffusion	2019	Norman Schmitz
+	Fractional Diffusion Models of Anomalous Transport	2008	D. del-Castillo-Negrete
+	Anomalous Diffusive Behavior in Fractional Dynamics	2003	Kyungsik Kim Jum Soo Choi Yong Sae Kong
+	A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative	2023	Bo Tang Yanping Chen Bin Xie Xiuxiu Lin
+	Diffusion in a heterogeneous system, fractional dynamics and anomalous diffusion	2019	E. K. Lenzi Marcelo Kaminski Lenzi Rafael S. Zola

Works That Cite This (441)

Action	Title	Year	Authors
+	The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation	2018	Shujun Shen Fawang Liu Vo Anh
+ PDF Chat	Exponential-sum-approximation technique for variable-order time-fractional diffusion equations	2021	Jiali Zhang Zhi-Wei Fang Hai‐Wei Sun
+ PDF Chat	Variable order fractional Fokker–Planck equations derived from Continuous Time Random Walks	2018	Peter Straka
+ PDF Chat	On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction–diffusion equation with delay	2022	Karel Van Bockstal Mahmoud A. Zaky Ahmed S. Hendy
+ PDF Chat	Numerical Study of Some Intelligent Robot Systems Governed by the Fractional Differential Equations	2019	Boya Zhou Wei Gu
+ PDF Chat	A numerical method for solving variable-order solute transport models	2020	Marjan Uddin Islam Ud Din
+ PDF Chat	On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application	2023	Hasib Khan Jehad Alzabut Haseena Gulzar Osman Tunç Sandra Pinelas
+ PDF Chat	Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions	2022	Jiali Zhang Zhi-Wei Fang Hai‐Wei Sun
+	Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis	2023	Abdulaziz Khalid Alsharidi Saima Rashid S.K. Elagan
+ PDF Chat	An Analysis and Global Identification of Smoothless Variable Order of a Fractional Stochastic Differential Equation	2023	Qiao Li Xiangcheng Zheng Hong Wang Zhiwei Yang Xu Guo

Works Cited by This (29)

Action	Title	Year	Authors
+	None	2002	Carl F. Lorenzo Tom T. Hartley
+	Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation	2008	Gerardo Dı́az Carlos F.M. Coimbra
+	Fractional diffusion in inhomogeneous media	2005	Aleksei V. Chechkin Rudolf Gorenflo Igor M. Sokolov
+	Implicit difference approximation for the time fractional diffusion equation	2006	Peixian Zhuang F. Liu
+	Fractional diffusion and Lévy stable processes	1997	Bruce J. West Paolo Grigolini Ralf Metzler Theo F. Nonnenmacher
+	Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights	2008	Aleksei V. Chechkin V.Yu. Gonchar Rudolf Gorenflo Nickolay Korabel Igor M. Sokolov
+	Mean fractional-order-derivatives differential equations and filters	1995	Michèle Caputo
+	Mittag–Leffler stability of fractional order nonlinear dynamic systems	2009	Yan Li YangQuan Chen Igor Podlubný
+ PDF Chat	Fractional diffusion equation for a power-law-truncated Lévy process	2004	Igor M. Sokolov Aleksei V. Chechkin J. Klafter
+ PDF Chat	Diffusion on multifractals	2005	Vo Anh J. M. Angulo M. D. Ruiz‐Medina