Existence Results for an Implicit Coupled System Involving $\xi$-Caputo and $p$-Laplacian Operators

This paper aims to establish the existence and uniqueness of a solution to a coupled system of $\xi$-Caputo fractional differential equations involving the $p$-Laplacian operator in an arbitrary Banach space. The results of the existence derived using the tools of topological degree theory for condensing maps and the Banach contraction principle. An illustrative example is given at the end to demonstrate the practical application of the theoretical results.