Nabla Fractional Derivative and Fractional Integral on Time Scales

TL;DR

This paper introduces nabla fractional derivatives and integrals on time scales, extending fractional calculus concepts in Riemann-Liouville and Grünwald-Letnikov senses, and discusses their fundamental properties.

Contribution

It presents new definitions of nabla fractional derivatives and integrals on time scales, expanding fractional calculus frameworks.

Findings

Defined nabla fractional derivatives and integrals on time scales

Established basic properties and theorems of nabla fractional calculus

Extended fractional calculus to the time scales setting

Abstract

In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties and theorems related to nabla fractional calculus are discussed.