Method of discretizing of fractional-derivative linear systems of ordinary differential equations with constant coefficients

TL;DR

This paper develops an exact discretization method for linear systems of fractional-derivative differential equations with constant coefficients, addressing the challenge that the resulting discrete system lacks constant matrix coefficients.

Contribution

It introduces a novel exact discretization approach for fractional-derivative systems with constant coefficients, including comparison with existing approximate methods and applications to controlled systems.

Findings

The method provides an exact discretization scheme.

Comparison shows advantages over approximate methods.

Numerical examples illustrate practical applicability.

Abstract

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in this case does not have constant matrix coefficients. Further, this method is compared with the known approximate method. The above scheme is developed for arbitrary linear systems with piecewise constant perturbations. The results are applied to the discretization of linear controlled systems and are illustrated with numerical examples.