On a Hilfer fractional differential equation with nonlocal Erd\'{e}lyi-Kober fractional integral boundary conditions

TL;DR

This paper studies a Hilfer fractional differential equation with nonlocal Erdélyi-Kober fractional integral boundary conditions, establishing existence, uniqueness, and stability results using fixed point theorems, supported by an illustrative example.

Contribution

It introduces new existence, uniqueness, and stability results for a specific fractional differential equation with nonlocal boundary conditions, applying fixed point theorems.

Findings

Proved existence and uniqueness of solutions.

Established Ulam-Hyers stability.

Provided an example illustrating the results.

Abstract

We consider a Hilfer fractional differential equation with nonlocal Erd\'{e}lyi-Kober fractional integral boundary conditions. The existence, uniqueness and Ulam-Hyers stability results are investigated by means of the Krasnoselskii's fixed point theorem and Banach's fixed point theorem. An example is given to illustrate the main results.