Recursive Local Fractional Derivative

TL;DR

This paper generalizes the local fractional derivative to higher orders, enhancing Taylor expansion accuracy and extending the product rule's applicability in fractional calculus.

Contribution

It introduces a generalized definition of the local fractional derivative for orders beyond the critical order, improving approximation and rule validity.

Findings

Enhanced local fractional Taylor expansion accuracy

Extended validity of the product rule in fractional calculus

Broader applicability of fractional derivatives

Abstract

The definition of the local fractional derivative has been generalised to the orders beyond the critical order. This makes it possible to retain more terms in the local fractional Taylor expansion leading to better approximation. This also extends the validity of the product rule.