On the Existence and Uniqueness Theory: A Generalized Fractional Impulsive p-Laplacian BVP

Abstract This work investigates the boundary value problem (BVP) of impulsive differential equations (DEs) with a nonlinear ρ−Caputo fractional and p-Laplacian operator. To prove the existence and uniqueness of solutions, we employ Schauder’s and Schaefer’s fixed point theorems, along with the Banach contraction principle. Additionally, we present two examples to show the practical applications and significance of our main results. Our study provides a new perspective on impulsive DEs with fractional and p–Laplacian operators and contributes to the development of the theory of impulsive DEs. AMS Subject Classi cation: Primary 34A08; 34B15; secondary 34B27