A numerical scheme for initial compliance and creep response of a system

This paper is an extension of a previous paper [Yuan, L., Agrawal, O. P., 2002. A numerical scheme for dynamic systems containing fractional derivatives. Journal of Vibration and Acoustics 124, 321-324] in which we demonstrated that a fractional differential equation (FDE) governing the dynamics of a system could be transformed into a set of differential equations with no fractional derivative terms. We developed a memory free formulation (MFF) for FDEs and eliminated the need of storing long memory. In this paper, we reexamine the MFF for FDEs and address some of the concerns raised by various authors about the formulation. The new formulation allows accurate computation of initial compliance and creep response of a system for a long duration. The performance of the scheme is demonstrated using an example. Possible future directions of research are discussed. It is hoped that the benefits of the MFF for FDEs will initiate further research in this direction.