Existence and uniqueness of solutions of Hilfer fractional neutral impulsive stochastic delayed differential equations with nonlocal conditions

Abstract In this work, we investigate the existence and uniqueness of solutions to Hilfer fractional neutral impulsive stochastic delayed differential equations with nonlocal conditions. These equations, which are characterized by Hilfer fractional derivatives, stochastic perturbations, impulses, delays, and nonlocal components, naturally occur in a number of practical domains, including signal processing, control theory, and systems with memory and abrupt transitions. Krasnoselskii’s fixed point theorem is used to prove the existence of solutions, and the Banach contraction principle guarantees uniqueness. Two examples with particular parameter values are analyzed to show how the theoretical results are applicable. Graphical analysis is used to show how the solutions behave dynamically under different stochastic and impulsive inputs. Furthermore, simulations provide further details about the qualitative behavior of the solutions. By providing new insights into the theory of fractional stochastic differential equations with complex structures, this work broadens the potential applications of these equations in simulating real-world events.