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

Advances in Difference Equations

article

Ahmadi, Zahra¹  Lashkaripour, Rahmatollah¹  Baghani, Hamid¹  Heidarkhani, Shapour²  Caristi, Giuseppe³ 

[1] Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan;Department of Mathematics, Faculty of Sciences, Razi University;Department of Economics, University of Messina

关键词: Fixed point;    Sequential fractional differential equation;    The Banach fixed point theorem;    Measure of noncompactness;    Infinite system;   

DOI  :  10.1186/s13662-020-02682-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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 $c_{0}$ and $\ell_{p}$ by applying the Darbo fixed point theorem. Moreover, the proposed method is applied to several examples to show the clarity and effectiveness.

【 授权许可】

CC BY