Validity of the fractional Leibniz rule on a coarse-grained medium yields a modified fractional chain rule

TL;DR

This paper demonstrates that the Leibniz rule's validity on a coarse-grained medium leads to a modified fractional chain rule, aligning with alternative fractional calculus approaches, and compares these findings to recent related work.

Contribution

It introduces a modified fractional chain rule derived from the validity of the Leibniz rule on coarse-grained media, connecting it with existing fractional calculus theories.

Findings

Validity of Leibniz rule implies a modified chain rule

Comparison with recent fractional calculus research

Alignment with alternative fractional calculus versions

Abstract

In this short communication, we show that the validity of the Leibniz rule for a fractional derivative on a coarse-grained medium brings about a modified chain rule, in agreement with alternative versions of fractional calculus. We compare our results to those of a recent article on this matter.