Qualitative Results for Nonlocal Fractional Hilfer Boundary Value Problems (BVP) using Fixed Point Theory

Abstract

The work in this study focuses upon the qualitative analysis of the nonlinear boundary value problem (BVP) via Hilfer fractional derivative. This study demonstrates the qualitative results for the uniqueness and existence of a solution utilizing the concepts of fixed point theory comprising Banach, Schaefer, and Krasnoselskii’s fixed point theorem. Subsequently, the stability of the solution of the amused differential equations is proposed via the theory of Ulam Hyers (UH) stability which adds significance to the quality of the findings. In order to demonstrate the application and validation of the derived results some numerical examples are also provided.