A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives

Abstract

Abstract This paper presents a numerical scheme for dynamic analysis of mechanical systems subjected to damping forces which are proportional to fractional derivatives of displacements. In this scheme, a fractional differential equation governing the dynamic of a system is transformed into a set of differential equations with no fractional derivative terms. Using Laguerre integral formula, this set is converted to a set of first order ordinary differential equations, which are integrated using a numerical scheme to obtain the response of the system. Numerical studies show that the solution converges as the number of Laguerre node points are increased. Further, results obtained using this scheme agree well with those obtained using an analytical technique.