Existence and Ulam type stability for nonlinear Riemann–Liouville fractional differential equations with constant delay

Abstract

A nonlinear Riemann–Liouville fractional differential equation with constant delay is studied. Initially, some existence results are proved. Three Ulam type stability concepts are defined and studied. Several sufficient conditions are obtained. Some of the obtained results are illustrated on fractional biological models.

Keywords

• riemann–liouville fractional derivative
• constant delay
• initial value problem
• existence
• ulam type stability