A Coupled System of Caputo–Hadamard Fractional Hybrid Differential Equations with Three-Point Boundary Conditions

Abstract

This article presents a study of the existence and uniqueness of solutions for a system of hybrid fractional differential equations involving fractional derivatives of the Caputo-Hadamard type with three-point hybrid boundary conditions. In addition to this, the “Hyres–Ulam” stability of the solutions for this type of equation is verified, and finally a numerical example was presented to support our theoretical results.

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

“…Due to the importance of the subject and the possibility of employing it in various scientifc felds, many researchers in the feld of fractional diferential have studied the systems of fractional diferentials equations with a variety of serious conditions accompanying them. For more information about, these scientifc papers, the reader can see [24][25][26][27][28][29][30][31], and the stability of solutions was studied after the existence of them. To enrich the reader, it is possible to see [32][33][34].…”

A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

“…Due to the importance of the subject and the possibility of employing it in various scientific fields, many researchers in the field of fractional differential have studied the systems of FDEs with a variety of serious conditions accompanying them. For more information on these scientific papers, the reader can see [26][27][28][29][30][31][32][33], A large group of researchers interested in FCs studies the stability of solutions for FDEs after studying the existence of their solutions. To enrich the reader, it is possible to see [34][35][36].…”