Electromechanical stability and T-controllability of Hilfer fractional stochastic switching systems using integral contraction framework

This paper investigates the existence, uniqueness, and Hyers–Ulam stability of a new class of higher-order coupled stochastic non-instantaneous impulsive Hilfer fractional switched differential equations with deviated arguments and Poisson jumps in finite-dimensional spaces. The well-posedness of the system is established using the method of integral contractors under suitable regularity assumptions and a weakened Lipschitz-type condition on the nonlinear operators. The proposed framework introduces a unified class of coupled Hilfer fractional stochastic switching systems that incorporates non-instantaneous impulses, switching dynamics, fractional integral initial conditions, and both continuous and jump-type stochastic perturbations. This structure provides a mathematically consistent and physically realistic model for hybrid dynamical systems with memory and random disturbances. The analysis employs techniques from fractional calculus, stochastic analysis, Laplace transforms, and Mittag–Leffler function theory. A numerical example and an application to electromechanical coupling and seeker stabilisation are presented to illustrate the effectiveness and practical relevance of the theoretical results.