On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the $\psi$-Hilfer operator

TL;DR

This paper investigates the existence, uniqueness, and stability of solutions for nonlinear fractional differential equations involving the $$-Hilfer operator, with applications demonstrated through examples.

Contribution

It introduces new results on the Ulam-Hyers and Ulam-Hyers-Rassias stability for equations with the $$-Hilfer fractional derivative, expanding understanding of their solution behavior.

Findings

Proved existence and uniqueness of solutions.

Established stability conditions for solutions.

Provided illustrative examples of applications.

Abstract

We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the $\psi$-Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions. A few examples are presented in order to illustrate the possible applications of our main results.