Existence and uniqueness of solution for a fractional Riemann–Liouville initial value problem on time scales

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.

Keywords

• Fractional derivatives
• Dynamic equations
• Initial value problems
• Time scales