Trajectory Controllability of Higher‐Order Coupled Stochastic Switched Systems Involving Hilfer Fractional Derivatives and Non‐Instantaneous Impulses via Measures of Noncompactness

ABSTRACT This paper investigates the solvability and trajectory controllability of higher‐order Hilfer fractional coupled stochastic non‐instantaneous impulsive switched differential equations with deviated arguments in the finite‐dimensional space. The first part focuses on analyzing the existence of solutions using the Mönch fixed‐point theorem. In the second part, the strongest notion, called trajectory 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. A numerical example is provided to validate the obtained theoretical results.