On qualitative theory of fractional order delay evolution equation via the prior estimate method

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.