On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions

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.

Ulam–Hyers Stability and Uniqueness for Nonlinear Sequential Fractional Differential Equations Involving Integral Boundary Conditions

“…Proof. The general solutions of the sequential fractional differential equations [20][21][22][23] in (3) are known as:…”

On a Coupled System of Fractional Differential Equations via the Generalized Proportional Fractional Derivatives

“…Baitiche et al [34] discussed the existence and uniqueness of solutions to some nonlinear fractional differential equations involving the ψ-Caputo fractional derivative with multipoint boundary conditions. Mahmudov et al [35] investigated existence and uniqueness results for a coupled system of Caputo fractional differential equations with integral boundary conditions. Some existing frameworks mentioned above encourage us to study the following coupled system of fractional differential equations:…”

Stability, Existence and Uniqueness of Boundary Value Problems for a Coupled System of Fractional Differential Equations

“…Moreover, λ i , µ i , i = 1, 2, are real constants with λ i µ i 1 and f , g : [0, T] × R × R → R are appropriately chosen functions. For further details on this topic, refer to References [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”