Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

Abstract

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

Keywords

• riemann-liouville fractional derivative
• initial value problem
• existence
• uniqueness
• ulam stability
• fixed point theorem
• 26a33