Total controllability of stochastic non-instantaneous impulsive Hilfer fractional switched dynamic systems with deviated arguments

This article investigates the solvability and controllability of stochastic non-instantaneous impulsive Hilfer fractional switched differential equations with deviated arguments and fractional Brownian motion (fBm) in the finite-dimensional space. The first part focuses on analyzing the existence and uniqueness of solutions using the Banach fixed-point theorem. In the second part, controllability results are established for the considered system. This study introduces a new class of control functions designed to govern the system at the termination of time intervals and on each impulsive event, incorporating stochastic noise. This approach leads to comprehensive controllability outcomes, often termed as total controllability results. The theoretical results are primarily established using fixed-point theorem, fractional calculus, Laplace transform, stochastic analysis, and Mittag-Leffler function. A numerical example is provided to validate the obtained theoretical results.