Existence of solution for Hilfer fractional differential problem with nonlocal boundary condition

TL;DR

This paper investigates the existence of solutions for Hilfer fractional differential equations with nonlocal boundary conditions using fixed point theorems and measures of noncompactness, supported by an illustrative example.

Contribution

It introduces a new approach combining fixed point theorems and noncompactness measures to establish solution existence for Hilfer fractional problems with nonlocal boundaries.

Findings

Existence of solutions is proven under certain conditions.

The method applies to a class of Hilfer fractional differential equations.

An illustrative example demonstrates the applicability of the results.

Abstract

This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition. We use the equivalent integral equation to study the considered Hilfer differential problem with nonlocal boundary condition. The Monch type fixed point theorem and the measure of the noncompactness technique are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example.