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

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