Abstract
In this manuscript we use prior estimate method also known as the topological degree method to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with proportional delay using Caputo derivative. In the same line, we will also study different kinds of Ulam stability such as Ulam-Hyers (UH) stability, generalized Ulam-Hyers (GUH) stability, Ulam-Hyers-Rassias (UHR) stability, and generalized Ulam-Hyers-Rassias (GUHR) stability for the considered problem. To justify our results, we provide a pertinent example.