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A numerical scheme for initial compliance and creep response of a system. (English) Zbl 1258.74090
Summary: This paper is an extension of a previous paper [L. Yuan and O. P. Agrawal, J. Vib. Acoust. 124, 321–324 (2002)] 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.

MSC:
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74K99 Thin bodies, structures
26A33 Fractional derivatives and integrals
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