(untitled) (Global Journal of Sciences, 2025)
This paper establishes Ulam-Hyers stability for first-order switched Volterra integro-differential equations under average dwell time switching constraints. We analyze systems of the form:y′(t)=pσ(t)(t)y(t)+qσ(t)(t)+∫0tKσ(t)(t,s)y(s) ds,t∈[0,T]y′(t) = p_σ(t)(t)y(t) + q_σ(t)(t) + _0^t K_σ(t)(t, s)y(s) ds,t [0, T]y′(t)=pσ(t)​(t)y(t)+qσ(t)​(t)+∫0t​Kσ(t)​(t,s)y(s)ds,t∈[0,T]where σ(t):[0,T]→1,…,Nσ(t) : [0, T] → {1, …, N}σ(t):[0,T]→1,…,N is a switching signal with average dwell time τa>0τ_a > 0τa​>0. Using successive approximation methods, we prove existence and uniqueness of solutions while deriving explicit error bounds for approximate solutions. The stability constantC=T(N0+T/τa)e(M1+M2T)TC = T(N_0 + T/τ_a)e^(M_1 + M_2T)TC=T(N0​+T/τa​)e(M1​+M2​T)Tquantifies robustness by incorporating switching parameters, kernel bounds, and the time horizon. Our results extend classical integro-differential equation theory to switched systems with memory effects, providing a foundation for robust control design in applications such as power electronics, biological processes, and thermal management systems.