Existence of solutions of infinite system of nonlinear sequential fractional differential equations

Zahra Ahmadi, Rahmatollah Lashkaripour, Hamid Baghani, Shapour Heidarkhani, Giuseppe Caristi

Type: Article

Publication Date: 2020-05-19

Citations: 3

DOI: https://doi.org/10.1186/s13662-020-02682-1

Abstract

Abstract In a recent paper (Filomat 32:4577–4586, 2018) the authors have investigated the existence and uniqueness of a solution for a nonlinear sequential fractional differential equation. To present an analytical improvement for Fazli–Nieto’s results with some conditions removed based on a new technique is the main objective of this paper. In addition, we introduce an infinite system of nonlinear sequential fractional differential equations and discuss the existence of a solution for them in the classical Banach sequence spaces $c_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> and $\ell_{p}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ℓ</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math> by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness.

Locations

Advances in Difference Equations - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View

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