On local generalized Ulam-Hyers stability for nonlinear fractional functional differential equation (Q779506)

Summary: We discuss the existence of positive solution for a class of nonlinear fractional differential equations with delay involving Caputo derivative. Well-known Leray-Schauder theorem, Arzela-Ascoli theorem, and Banach contraction principle are used for the fixed point property and existence of a solution. We establish local generalized Ulam-Hyers stability and local generalized Ulam-Hyers-Rassias stability for the same class of nonlinear fractional neutral differential equations. The simulation of an example is also given to show the applicability of our results.