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.
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.