Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives

Abstract

This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville−Caputo left generalized fractional derivative and the left generalized fractional derivative were used. The behaviors of the analytical solutions of the mass-spring-damper systems described by the left generalized fractional derivative and the Liouville−Caputo left generalized fractional derivative were represented graphically and the effect of the orders of the fractional derivatives analyzed. We finish by analyzing the global asymptotic stability and the converging-input-converging-state of the unforced mass-damper system, the unforced spring-damper, the spring-damper system, and the mass-damper system.

Keywords

• mass-spring-damper systems
• Liouville–Caputo generalized fractional derivative
• left generalized fractional derivative
• global asymptotic stability