Hyers-Ulam stability of uncertain fractional switched system

This paper investigates the Hyers-Ulam stability of uncertain fractional switched systems governed by Caputo-type fractional differential equations. Unlike classical switched systems, these incorporate subjective uncertainties through canonical processes. Building on uncertainty theory and fractional calculus, we establish sufficient conditions for Hyers-Ulam stability under linear growth and Lipschitz constraints. Our results generalize previous works on fractional switched systems by incorporating uncertainty propagation and switching dynamics into the stability analysis. A rigorous proof framework is developed using Banach fixed point theory and fractional integral inequalities. To demonstrate practical utility, we apply our results to a Modified Evans Economic Growth Model with switching dynamics. Stability bounds are computed across fractional orders, with explicit quantitative bounds derived (e.g., \(\kappa = S^p/[\Gamma(p+1)(1-\eta)]\)), validating theoretical predictions. Our work bridges uncertainty theory, switched systems, and stability analysis, offering new tools for robust fractional system design.