Modelling some real phenomena by fractional differential equations

TL;DR

This paper demonstrates that fractional differential equations, particularly those involving Caputo derivatives, can more effectively model certain real-world phenomena than traditional differential equations, using numerical optimization for parameter fitting.

Contribution

It introduces a numerical optimization method to determine the fractional order and parameters that best fit experimental data, highlighting the modeling advantages of fractional differential equations.

Findings

Fractional models fit experimental data better than integer-order models.

Numerical optimization effectively identifies optimal fractional orders.

Fractional differential equations provide more accurate descriptions of certain phenomena.

Abstract

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.