Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals

 Fractional differential equations of degree 1<α<2 are considered in this paper. A summary of numerical schemes for the time-domain solution of such problems is given. While all these methods require evaluation of the history of the state variables, an alternative concept recently published by Yuan and Agrawal (2002), which is computationally more efficient, is further developed. This scheme is based on a transformation of the original integro-differential problem into a system of linear differential equations. Here, parallels to the theory of internal variables are drawn. Received: 18 June 2002 / Accepted: 12 July 2002