What is the best fractional derivative to fit data?

TL;DR

This paper investigates how the choice of fractional derivative affects the accuracy of data modeling, demonstrating that selecting the appropriate derivative type improves model fit based on experimental data.

Contribution

It introduces a method to determine the most suitable fractional derivative for data modeling using least squares fitting across different derivative types.

Findings

Different fractional derivatives yield varying data fit qualities.

The optimal fractional derivative type depends on the specific data set.

Choosing the correct derivative improves modeling accuracy.

Abstract

The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the order of the fractional differential equation that better describes the experimental data, for different types of fractional derivatives.