Abstract
The study is on the existence of the solution for a coupled system of fractional differential equations with integral boundary conditions. The first result will address the existence and uniqueness of solutions for the proposed problem and it is based on the contraction mapping principle. Secondly, by using Leray–Schauder’s alternative we manage to prove the existence of solutions. Finally, the conclusion is confirmed and supported by examples.
Highlights
Fractional calculus and coupled fractional differential equations are amongst the strongest tools of modern mathematics as they play a key role in developing differential models for high complexity systems
In terms of developing high complexity models, applications of coupled fractional differential equations can be significantly extended by dealing with various types of integral boundary conditions
Integral boundary conditions are essential for obtaining reliable models in many practical problems, such as regularization of parabolic inverse problems [15] and flow analysis in computational fluid dynamics [16]
Summary
Fractional calculus and coupled fractional differential equations are amongst the strongest tools of modern mathematics as they play a key role in developing differential models for high complexity systems. In [27], the authors investigated the existence and uniqueness of solutions for the coupled system of nonlinear fractional differential equations with three-point boundary conditions, given below:. In a study [28], the following coupled system of nonlinear fractional differential equations, with the given boundary conditions was studied:. Where D k denote the Caputo fractional derivatives of order k,and f , g : [0, T ] × R3 → R, are given continuous functions, and ρ1 , ρ2 , μ1 , μ2 are real constants.
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