Linearized Asymptotic Stability of Caputo-Katugampola Fractional Integro differential Equations

In this article a linearized asymptotic stability theorem is established for a generalized fractional integrodifferential equation involving Caputo-Katugampola 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 allows us to directly reconstruct the main problem into a unique parameter dependent fixed point formulation consisting of Mittag Leffler functions with simple diagonal matrix arguments, making it easier to arrive at the estimates. The Banach fixed point technique is then used to establish the stability.