Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator

In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions G^α₁(t,s) , G^β₁(t,s) , G^α₂(t,s) , G^β₂(t,s) . Then using topological degree theory and Leray-Schauder’s-type fixed point theorem, existence and uniqueness results are proved. An illustrative and expressive example is given as an application of the results.