The study of nonlinear fractional boundary value problems involving the p-Laplacian operator

Abstract

Abstract The p-Laplacian has attracted considerable attention in numerous fields such as mechanics, image processing and game theory. It is a nonlinear operator which has been used in the modelling and qualitative aspects in numerous problems. In this research work, we propose a new nonlinear fractional differential equation involving the p-Laplacian, which include the generalized Caputo fractional derivatives. We investigate the existence and uniqueness of solutions to our proposed problem through the application using the Banach and Schauder’s fixed-point theorems. Additionally, we illustrate the practical applicability of our findings by applying them to a specific example, thereby validating their efficacy.