Some analysis on a fractional differential equation involving a noncontinuous right-hand side

TL;DR

This paper develops new techniques to prove local existence and uniqueness for a nonlinear Riemann-Liouville fractional differential equation with a discontinuous right-hand side.

Contribution

It introduces novel methods to handle discontinuities in the nonlinear term of fractional differential equations, establishing foundational existence and uniqueness results.

Findings

Established local existence and uniqueness theorems

Handled nonlinear equations with discontinuous right-hand sides

Extended fractional differential equation theory to noncontinuous cases

Abstract

By developing new techniques we establish local existence and uniqueness theorems for an initial value problem involving a nonlinear equation in the sense of Riemann-Liouville fractional derivative in the case that the nonlinear function on the right hand side of the equation is not continuous on $[0,T]\times\mathbb{R}.$