  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.
