On the Existence and Stability of Solutions for a Class of Fractional Riemann–Liouville Initial Value Problems

This article deals with a class of nonlinear fractional differential equations, initial conditions, involving the Riemann–Liouville derivative order α∈(1,2). The main objectives are to obtain conditions for existence and uniqueness solutions (within appropriate spaces), analyze stabilities Ulam–Hyers Ulam–Hyers–Rassias types. In fact, different obtained based on analysis an associated integral equations distinct fixed-point arguments. Additionally, using Bielecki-type metric some additional contractive arguments, also guarantee problems under analysis. Examples included illustrate theory.