A coupled system of fractional differential equations with nonlocal integral boundary conditions

Abstract

In this paper, we prove the existence and uniqueness of solutions for a system of fractional differential equations with Riemann-Liouville integral boundary conditions of different order. Our results are based on the nonlinear alternative of Leray-Schauder type and Banach's fixed-point theorem. An illustrative example is also presented.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

“…The study of coupled systems of fractional order differential equations is also very significant as such systems appear in a variety of problems of applied nature, especially in biosciences. For details and examples, the reader is referred to the papers [3], [18], [21], [22], [23] and the references cited therein.…”

Existence result for a class of coupled fractional differential systems with integral boundary value conditions

“…As a result, fractional differential equations have attracted much attention, and lots of good results have been obtained. See [2][3][4][5][8][9][10][11] for a good overview.…”

“…Meanwhile, coupled fractional differential systems have been studied in some recent works [8,13,14]. For example, in [8], the authors studied the following coupled system of fractional differential equations with nonlocal integral boundary conditions where D α 0 + is the standard Riemann-Liouville fractional derivative, 1 < α, β 2, 0 < η 1 , η 2 < 1,…”

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

“…The motivation for those works stems from both the intensive development of the theory of fractional calculus itself and the applications. See for example [26]- [30] where systems for fractional differential equations were studied by using Banach contraction mapping principle and Schaefer's fixed point theorem.…”