Fractional impulsive differential systems: Stochastic perspectives with nonlocal conditions

Abstract

This study delves into the analysis of a class of stochastic fractional neutral differential equations characterized by Gaussian noise, impulse effects, and nonlocal conditions. These equations capture complex phenomena in various fields, including physics, engineering, and biology, making their investigation particularly valuable. We employ rigorous mathematical methods to address the existence and stability of solutions in the presence of these intricate components. In addition to establishing the existence and uniqueness of solutions, we delve into the stability of these solutions using mathematical tools and theorems. An example is provided to substantiate our results. The investigation utilizes the extensive knowledge of fractional calculus and stochastic processes, along with established findings in the examination of nonlocal and impulsive systems.