Existence Results for $\aleph$-Caputo Fractional Boundary Value Problems with $p$-Laplacian Operator

Author:

Batit Özen Özlem1ORCID

Affiliation:

1. EGE ÜNİVERSİTESİ

Abstract

This study delves into the investigation of positive solutions for a specific class of $\aleph$-Caputo fractional boundary value problems with the inclusion of the p-Laplacian operator. In this research, we use the theory of the fixed point theory within a cone to establish the existence results for solutions of nonlinear $\aleph$-Caputo fractional differential equations involving the p-Laplacian operator. These findings not only advance the theoretical understanding of fractional differential equations but also hold promise for applications in diverse scientific and engineering disciplines. Furthermore, we provide a clear and illustrative example that serves to reinforce the fundamental insights garnered from this investigation.

Publisher

Gaziosmanpasa University

Reference15 articles.

1. A. E. Mfadel, S. Melliani, M. Elomari, Existence and uniqueness results for $\psi$-caputo fractional boundary value problems involving the $p$ Laplace operator, UPB Scientific Bulletin Series A: Applied Mathematics and Physics 94 (2022) 37-46.

2. M. S. Abdo, A. G. Ibrahim, S. K. Panchal, Nonlinear implicit fractional differential equation involving $\psi$-Caputo fractional derivative, Proceeding of the Jangjeon Mathematical Society 22 (3) (2019) 387-400.

3. R. Almeida, A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation 44 (2017) 460-481.

4. M. S. Abdo, S. K. Panchal, A. M. Saeed, Fractional boundary value problem with $\psi$-Caputo fractional derivative, Proceedings Mathematical Sciences 129 (65) (2019) 64-78.

5. M. S. Abdo, S. K. Panchal, Fractional integro-differential equations involving $\psi$-Hilfer fractional derivative, Advances in Applied Mathematics and Mechanics 11 (2) (2019) 338-359.

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