Work

Existence and stability of solution for a coupled system of Caputo–Hadamard fractional differential equations

Year: 2024

Type: article

Abstract: In our present work, we study a coupled system of Caputo–Hadamard fractional differential equations supplemented with a novel set of initial value conditions involving the $\eta =(t\frac{d}{dt})$ derivatives. We provided sufficient criteria for the existence and stability of the solutions for a coupled system of fractional differential equations by applying the Hyers–Ulam stability theory, the fixed point theorems of Banach, Krasnoselskii, and the Leray–Schauder nonlinear alternative. When computing priori bounds in Leray–Schauder nonlinear alternative and stability of the solutions, a novel Gronwall type inequality related to Hadamard integral is employed. This study investigates the properties of a solution, such as existence, uniqueness, and stability, to a given problem without attempting to solve the exact solution, and its theoretical applications are illustrated by providing an example.

Source: Fixed Point Theory and Algorithms for Sciences and Engineering

DOI: 10.1186/s13663-024-00773-2

Authors: Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera

Institutions: Bule Hora University, Adama Science and Technology University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,590

OpenAlex ID: W4404894875