New results for a system of two fractional differential equations involving n Caputo derivatives

Abstract

This paper studies a coupled system of two differential equations of arbitrary orders using Caputo approach with n derivatives, n ∈ N * , n = 1. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

Existence and Uniqueness Results for a Coupled System of Hadamard Fractional Differential Equations With Multi-Point Boundary Conditions

“…On the other hand, existence and uniqueness of solutions to boundary value problems for fractional differential equations has attracted the attention of many authors, see for example, [16,17,19] and the references therein. Moreover, the study of coupled systems of fractional order is also important in various problems of applied nature [2,9,10,15,24,25]. Recently, many people have established the existence and uniqueness for solutions of some fractional systems, see [9,10,21,23,25] and the reference therein.…”

“…Moreover, the study of coupled systems of fractional order is also important in various problems of applied nature [2,9,10,15,24,25]. Recently, many people have established the existence and uniqueness for solutions of some fractional systems, see [9,10,21,23,25] and the reference therein. In the last few decades, much attention has been focused on the study of the existence and uniqueness of solutions for boundary value problems of Riemann-Liouville type or Caputo type fractional differential equations, see [21,23,24,25].…”

On existence of solutions for fractional differential equations with nonlocal multi-point boundary conditions

“…Recently, much attention has been focused on the study of the existence of solutions for fractional differential equations with local boundary conditions by the use of techniques of nonlinear analysis (Banach contraction principle, Leray-Schauder and O'Regan lemmas, etc.) [5,11,17].…”

High dimensional fractional coupled systems: New existence and uniqueness results

“…In the literature, we can find many papers dealing with the existence and uniqueness of solutions. For more details, we refer the reader to [11,16,[18][19][20][21] and the references therein.…”