On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions

Abstract

We solve a coupled system of nonlinear fractional differential equations equipped with coupled fractional nonlocal non-separated boundary conditions by using the Banach contraction principle and the Leray-Schauder fixed point theorem. Finally, we give examples to demonstrate our results. MSC: 34A08; 34B15Keywords: Caputo fractional derivative; Nonlocal; Non-separated boundary conditions; Existence of solutionwhere c D q denotes the Caputo fractional derivative of order q, f is a given continuous function.

New Existence of Solutions for Fractional Integro-Differential Equations with Nonseparated Boundary Conditions

“…On the other hand, many papers have considered the nonseparated boundary conditions as they are a very important class of boundary value conditions (we refer the readers to [23][24][25][26][27][28]).…”

Analysis of a coupled system of fractional differential equations with non-separated boundary conditions

“…Li et al [18] investigated the existence and uniqueness of solutions to the following FDEs system with non-separated boundary conditions: [6] studied fractional order coupled systems with non-separated coupled boundary conditions: Recently, Rao and Alesemi [23] investigated the existence and uniqueness of solutions for a coupled system of fractional differential equations with fractional non-separated coupled boundary conditions. As far as we know, the Ulam-Hyers stability analysis for the solutions of nonlinear coupled FDEs with non-separated coupled boundary conditions has been rarely investigated.…”

Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions

“…Coupled systems of fractional differential equations play a key role in developing differential models such as the synchronization of chaotic systems [13][14][15], anomalous diffusion [16,17], disease models [18,19], ecological models [20], Lorenz system [21], and nonlocal thermoelectricity systems [22,23]. For recent theoretical results on the topic, we refer the reader to a series of papers [24][25][26][27][28][29][30][31][32][33][34][35][36][37] and the references cited therein. Ahmad and Ntouyas [32,33] discussed some fractional integral boundary value problems involving Hadamard fractional differential equations/systems and obtained the existence and uniqueness of solutions by applying the Banach fixed point theorem and Leray-Schauder alternative, respectively.…”