Existence of solution for Hilfer fractional differential equations with boundary value conditions

TL;DR

This paper establishes the existence of solutions for nonlinear Hilfer fractional differential equations with boundary conditions using fixed point theorems, providing a new approach with minimal assumptions and illustrative examples.

Contribution

It introduces a novel method for proving existence of solutions to Hilfer fractional boundary value problems under minimal conditions on the nonlinear function.

Findings

Existence of solutions is proven using Schauder, Schaefer, and Krasnoselski fixed point theorems.

An equivalent integral form of the boundary value problem is derived.

Results are validated through illustrative examples.

Abstract

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of continuous functions. Then we obtain the existence results for a given problem under a new approach and minimal assumptions on nonlinear function f. The technique used in the analysis relies on a variety of tools including Schauder, Schaefer and Krasnoselski fixed point theorems. We demonstrate our results through illustrative examples.