Existence, Uniqueness, and Stability of Solutions to Variable Fractional Order Boundary Value Problems

Year 2022, Issue: 41, 82 - 93, 31.12.2022

Mohammed Said Souıd , Zoubida Bouazza Ali Yakar

https://doi.org/10.53570/jnt.1182795

Cited By: 3

Abstract

This paper investigates the sufficient conditions for the existence and uniqueness of a class of Riemann-Liouville fractional differential equations of variable order with fractional boundary conditions. The problem is converted into differential equations of constant orders by combining the concepts of generalized intervals and piecewise constant functions. We derive the required conditions for ensuring the uniqueness of the problem in order to utilize the Banach fixed point theorem. The stability of the obtained solution in the Ulam-Hyers-Rassias (UHR) sense is also investigated, and we finally provide an illustrative example.

Keywords

Existence, uniqueness, stability, boundary value problems, fractional calculus

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