Solvability and stability for fractional differential equations involving two Riemann-Liouville fractional orders

Abstract

In this work we study existence, uniqueness and Ulam-type stability for nonlinear fractional differential equations involving two Riemann-Liouville fractional derivatives. The existence and uniqueness of solutions is established by Banach’s fixed point theorem, whereas the existence of solutions is derived from Schaefer’s fixed point theorem. Furthermore, we present and discuss different types of Ulam stability. At the end, some illustrative examples are presented.