Existence and Ulam Stability Results for Two-orders Fractional Differential Equation

Abstract

In this paper, we deal with the existence of a unique solution and some Ulams type stability concepts for an initial value problem of a class of two-orders fractional di¤erential equations involving Caputos fractional derivative. We investigate two types of Ulam stability: Ulam-Hyers stability and Ulam-Hyers-Rassias stability for the considered problem of two fractional orders. We use the Banach xed point theorem and fractional calculus. Finally, we give an example to illustrate the results.