On Coupled System of Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations

TL;DR

This paper investigates the existence of solutions for coupled systems of $ ext{ extPsi}$-Hilfer hybrid fractional differential equations using fixed point theorems, with applications demonstrated through concrete examples.

Contribution

It introduces new existence results for coupled $ ext{ extPsi}$-Hilfer hybrid FDEs using fixed point theorems in Banach algebra, extending current fractional differential equations theory.

Findings

Established existence of solutions for IVP and BVP of coupled $ ext{ extPsi}$-Hilfer hybrid FDEs.

Provided concrete examples demonstrating the applicability of the theoretical results.

Extended the use of fixed point theorems to coupled fractional differential systems.

Abstract

This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of $\Psi$-Hilfer hybrid fractional differential equations (FDEs) and boundary value problem (BVP) for a coupled system of $\Psi$-Hilfer hybrid FDEs. Analysis of the current paper depends on the two fixed point theorems involving three operators characterized on Banach algebra. In the view of an application, we provided concrete examples to exhibit the effectiveness of our achieved results.