On implicit φ-Hilfer fractional differential equations with the p-Laplacian operator

Abstract

In this paper, we establish the existence and uniqueness of solutions for a new class of nonlocal boundary implicit φ-Hilfer fractional differential equations involving the p-Laplacian operator. The existence results are derived using the topological degree method for condensing maps and the Banach contraction principle. Moreover, we investigate the Ulam-Hyers and generalized Ulam-Hyers stability of our main problem. To illustrate the applicability of our theoretical results, we provide an example.