Existence and Stability of Implicit Fractional Differential Equations Involving the p-Laplacian Operator and Their Applications

Abstract The main objective of this paper is to establish the existence, uniqueness, and stability of implicit fractional differential equations involving a p-Laplacian operator, utilizing the Caputo-Katugampola fractional derivative. A novel approach is employed to examine the existence and uniqueness of solutions to the problem through fixed-point theorems. These results are original and extend several existing findings in the literature. Finally, an application is provided to illustrate the theoretical results.