Triple Positive Solutions and Nonexistence Results for Mixed Fractional Differential Equations with p-Laplacian Operator

In this paper, we investigate the existence of multiple positive solutions for a class of nonlinear fractional boundary value problems involving mixed fractional derivatives with a p-Laplacian operator. The analysis is carried out by combining Green’s function techniques with a generalized Avery-Henderson fixed point theorem in cones, which enables us to establish the existence of at least three positive solutions for the considered problem. Moreover, we derive eigenvalue-type conditions under which the associated problem admits no positive solutions. Finally, the theoretical results are illustrated and validated through several representative examples, clarifying the applicability of the obtained theoretical results.