Existence and Uniqueness of Solution for a Fractional Riemann-Liouville Initial Value Problem on Time Scales

TL;DR

This paper introduces a fractional Riemann-Liouville derivative on time scales, establishing its fundamental properties and proving existence and uniqueness of solutions for related initial value problems on arbitrary time scales.

Contribution

It defines a new fractional derivative operator on time scales and proves fundamental properties along with existence and uniqueness results for initial value problems.

Findings

Defined fractional Riemann-Liouville derivative on time scales

Proved fundamental properties of the new operator

Established existence and uniqueness of solutions for fractional initial value problems

Abstract

We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value problem on an arbitrary time scale.