A qualitative exploration of a coupled system with mixed fractional derivatives and the Laplacian operator

Abstract

This study focuses on the existence and uniqueness of solutions for a newly identified class of coupled systems, as well as its generalization. The systems incorporate mixed fractional derivatives, which combine Riemann-Liouville and Caputo fractional derivatives of varying orders, together with the Laplacian operator. We employ the Leray-Schauder alternative fixed point theorem within generalized Banach spaces and the Banach contraction principle as our primary analytical tools. Furthermore, we analyze the stability of the proposed coupled system in the context of Ulam-type stability. To illustrate the theoretical findings and results, we conclude with a practical example.