Existence of extremal solutions for mixed nonlinear fractional differential equations with p-Laplacian

Abstract

In this study, we establish the existence of minimal and maximal solutions for a class of mixed fractional differential equations involving the p-Laplacian operator, under appropriate boundary conditions. The nonlinear term is assumed to be continuous. By employing the method of upper and lower solutions together with a monotone iterative approach, we investigate the existence of extremal solutions. To demonstrate the effectiveness and applicability of the theoretical results, an illustrative example is included.