Topological Degree Method for a Coupled System of $\psi$-fractional Semilinear Differential Equations with non Local Conditions

Abstract

This paper explores the existence of solutions for non-local coupled semi-linear differential equations involving $\psi$-Caputo differential derivatives for an arbitrary $l\in (0,1)$. We use topological degree theory to condense maps and establish the existence of solutions. This theory allows us to relax the criteria of strong compactness, making it applicable to semilinear equations, which is uncommon. Additionally, we provide an example to demonstrate the practical application of our theoretical result.