On Multiplicative Fractional Calculus

TL;DR

This paper introduces the foundational concepts of multiplicative fractional calculus, defining various derivatives and integrals, and explores their properties and analogues to classical fractional calculus.

Contribution

It presents the first systematic development of multiplicative fractional derivatives and integrals, including Caputo, Riemann, Letnikov types, and their properties.

Findings

Defined multiplicative fractional derivatives and integrals.

Studied properties of these multiplicative operators.

Explored the multiplicative analogue of conformable fractional derivatives.

Abstract

We set the main concepts for multiplicative fractional calculus. We define Caputo, Riemann and Letnikov multiplicative fractional derivatives and multiplicative fractional integrals and study some of their properties. Finally, the multiplicative analogue of the local conformable fractional derivative and integral is studied.