Linearized asymptotic stability of implicit fractional integrodifferential system

This article establishes a linearized asymptotic stability theorem for an implicit fractional integrodifferential system involving Caputo fractional derivative. We use the method of Lyapunov–Perron fixed point formulation to study the stability of a linear autonomous system with a nonlinear Lipschitz perturbation. This method allows us to directly reconstruct the main problem into a unique parameter-dependent fixed point problem consisting of Mittag–Leffler functions with simple diagonal matrix arguments, making it easier to arrive at the estimates. Further, we use the Banach fixed point technique to establish the stability.