Stochastic stability of fractional-order quaternion-valued neural networks on time scales with general probabilistic bounded Markovian switching and neutral delays

This paper investigates the stochastic stability problem of fractional-order quaternion-valued neural networks (FOQVNNs) on time scales with general probabilistic bounded Markovian switching and neutral delays. Owing to the noncommutative nature of quaternion algebra and the coexistence of fractional dynamics, time-scale calculus, Markovian switching, and neutral delays, stability analysis becomes highly challenging, especially when conventional decomposition methods are employed. To overcome these difficulties, the considered system is treated directly in the quaternion domain without decomposition, thereby preserving the intrinsic algebraic structure and avoiding unnecessary dimensional expansion. By constructing an appropriate Lyapunov–Krasovskii functional and combining the free-weighting matrix technique with matrix inequality approaches, a sufficient condition guaranteeing stochastic stability for the considered FOQVNNs is derived and expressed as quaternion-valued linear matrix inequalities. The obtained criteria are general and can be efficiently verified by using a numerical example.