Existence and stability results for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions

TL;DR

This paper establishes existence, uniqueness, and stability results for a generalized coupled Hilfer fractional Langevin system with nonlocal boundary conditions, extending prior work by unifying Caputo and Riemann-Liouville derivatives.

Contribution

It introduces a more general fractional derivative framework using Hilfer derivatives, encompassing Caputo and Riemann-Liouville cases, and analyzes stability under these conditions.

Findings

Proved existence and uniqueness of solutions using fixed point theorems.

Established Ulam-Hyers and generalized Ulam-Hyers stability results.

Unified fractional derivative approach generalizes previous models.

Abstract

This paper deals with the existence and uniqueness of solution for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions. The novelty of this work is that it is more general than the works based on the derivative of Caputo and Riemann-Liouville, because when $\beta =0$ we find the Riemann-Liouville fractional derivative and when $\beta =1$ we find the Caputo fractional derivative. Initially, we give some definitions and notions that will be used throughout the work, after that we will establish the existence and uniqueness results by employing the fixed point theorems. Finaly, we investigate different kinds of stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability.