Algebraic Long-Time Decay in Fractional Classical Mechanics

Abstract

Time fractional formalism is a very useful tool in describing systems with memory and delay. In this article, we reformulate the equations presented in [F. Mainardi, Chaos Sol. Frac. 7(9) (1996) 1461-1477] and show that solutions for the relaxation and oscillation equations represent algebraic time-decaying behavior at asymptotic long time which depends on the order of time derivative.