Existence and Stability Results of Nonlinear Random Impulsive Integro-Differential Evolution Equations with Time-Varying Delays (Contemporary Mathematics, 2024)
This study examines the existence, uniqueness, and stability of the nonlinear random impulsive integrodifferential equations with time-varying delays under sufficient conditions. Our study is based on the Leray-Schauder alternative fixed point theorem, Pachpatte’s inequality, and the Banach contraction principle. Besides, we generalize, extend, and develop some results in the existing literature. Our approach is generalizing the results mentioned above and also achieving better results with lesser hypotheses by using the Leray-Schauder alternative fixed point theorem, Pachpatte’s inequality, and the Banach contraction principle.
Keywords: fixed point theorem; time-varying delays; integro-differential equations; random impulses; contraction principle