On more general forms of proportional fractional operators

TL;DR

This paper introduces new proportional fractional operators based on local proportional derivatives with respect to another function, expanding the mathematical framework of fractional calculus with potential applications in various fields.

Contribution

The paper proposes a novel class of proportional fractional operators generated from local proportional derivatives with respect to another function, including properties and kernel dependence.

Findings

Defined new proportional fractional operators with respect to another function

Established properties of these operators

Explored dependence on kernel functions

Abstract

In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also called proportional fractional operators of a function with respect to another function or proportional fractional operators with dependence on a kernel function.