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

Year 2024, Issue: 47, 61 - 71, 30.06.2024

Özlem Batit Özen

https://doi.org/10.53570/jnt.1472049

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.

Keywords

Fractional differential equation, boundary value problem, $p$-Laplacian operator, fixed point theorem

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