Existence and uniqueness results for mixed pantograph fractional differential equations equipped with the p-Laplacian operator with impulsive boundary conditions

Abstract

Mixed fractional boundary value problems with impulsive conditions have attracted significant attention due to their applications in various fields. In this study, we investigate the existence and uniqueness of solutions for a mixed fractional boundary value problem with impulsive conditions involving the \(\texttt{p}\)-Laplacian operator. The analysis is conducted using the Leray–Schauder and Banach fixed point theorems. Our theoretical findings confirm the existence and uniqueness of solutions under suitable assumptions. To illustrate the applicability of our results, two examples are provided at the end of the paper. The results contribute to the theory of fractional differential equations with impulsive effects and pave the way for further research on related nonlinear boundary value problems.