Determination of order in linear fractional differential equations

TL;DR

This paper investigates how the order of fractional derivatives affects the asymptotic behavior of solutions in linear fractional differential equations, emphasizing its importance for accurate system simulation.

Contribution

It introduces a method to determine the order of fractional derivatives based on the asymptotic decay rate of solutions.

Findings

Decay rate of solutions depends on the fractional order

Asymptotic expansion reveals the influence of derivative order

Numerical results validate the theoretical formulas

Abstract

In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great importance in an accurately appropriate simulation of the system under study. Specifically, by representing the asymptotic expansion of the solution, it could be obviously demonstrated that the decay rate of the solution is in influenced by the order of fractional differentiation. The numerical investigation is conducted into the proven formulas.