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

Abstract

In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Followed by a study of the stability of this solution using the Ulam-Hyres technique. This study concludes with an applied numerical example that helps in understanding the theoretical results obtained.

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

“…Next, to exam the values p 1 (t), p 2 (t) and p 3 (t) for θ 1 (t) = ln(t) and θ 2 (t) = (ln(t)) 2 , from the Equation ( 27), we obtain ϵ 1 = 0.75 and ϵ 2 = 0.0731058. The behavior of p 1 (t), p 2 (t), and p 3 (t) can be see in the Figures (3,4). Then by Theorem(3.5), the problem(34) is Ulam-Hyers stable.…”

“…The challenge of studying the existence and uniqueness solution is the study of its stability. Ulam-Hyers stability (UHS) is the most important types of stability is used in this field ( see [4,10,17,27,28,44], [7,25], [19]) Su [43], studied the existence of solutions for a coupled system of fractional differential equations:…”

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

“…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].…”