Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero

Abstract

In this article, we consider an initial value problem for a nonlinear differential equation with Riemann-Liouville fractional derivative. By proposing a new approach, we prove local existence and uniqueness of the solution when the nonlinear function on the right hand side of the equation under consideration is continuous on $(0,T]\times\mathbb{R}.$**********************************************************************************************************************************************************************************************************************************************************************************************