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

Walid Benhadda; Ali El Mfadel; Abderrazak Kassidi; M'hamed Elomari

doi:10.24193/subbmath.2025.4.05

Authors

Walid Benhadda Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
Ali El Mfadel Sultan Moulay Slimane University, Superior School of Technology, Khenifra, Morocco
Abderrazak Kassidi Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
M'hamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco.

DOI:

https://doi.org/10.24193/subbmath.2025.4.05

Keywords:

φ-Hilfer fractional derivative, Topological degree, pLaplacian operator, Ulam-Hyers stability.

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.

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