Affiliation:
1. Wuhan University of Technology
2. WUT
Abstract
A numerical method is proposed for calculating the fractional order derivative and successfully resolving the integrand singularity problem based on Zhang-Shimizu algorithm. And then a method is developed to calculate the twice nonlinear fractional derivative, numerical examples demonstrate the numerical method with high precision and good stability.
Publisher
Trans Tech Publications, Ltd.
Reference6 articles.
1. Wei Zhang, etc. Fractional Derivative and its Application in the Viscoelastic Theory of Hunan University (Natural Science Edition, Supplement), August 2001, Vol. 28, No. 4: 1-8.
2. Wei ZHANG and Nobuyuki SHIMIZU, Numerical Algorithm for Dynamic Problems Involving Fractional Operators, Int. J. of JSME, Ser. C, 41(1998), N0. 3, pp.364-370.
3. Zhang W, Shimizu N. FE formulation for the viscoelastic body modeled by fractional constitution law. Acta Mechanica Sinica, 2001, 17(4): 354-365.
4. Wei Zhang, Nobuyuki SHIMIZU and Hua Xu, Thermal effects of the viscoelastic materials described by fractional calculus constructive law[J]. The FIRST Asian conference on Multibody dynamics (2002).
5. Wei Zhang, Nobuyuki SHIMIZU. Damping properties of the viscoelastic material prescribed by fractional Kelvin-Voigt model [J]. JSME International Journal. Series C, 1999, VOL. 42, No. l.