A Study on the Existence and Uniqueness of Random Impulsive Hilfer Pantograph Differential Equations

Abstract

Nonlinear differential equations are crucial to models in natural and biological sciences, making them a vibrant and compelling area of research. Fractional differential equations are currently reformed and presented in various formats, establishing their core concepts within a mathematical framework and practical applications. The present work demonstrates the existence and uniqueness of solutions for Hilfer fractional pantograph differential equations with stochastic impulses utilizing fixed point theory. The Banach contraction principle indicates that the solution is unique, and the Lery-Schauder fixed point theorem examines if it exists. Furthermore, the qualitative behavior of the dynamical system has been investigated. Finally, it offers a theoretical implementation.