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A numerical method for fractional integral with applications

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Abstract

A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro-differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application, motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro-differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P. R. China

    Zhu Zheng-you & Cheng Chang-jun

  2. Department of Mathematics, Shanghai University, 200436, Shanghai, P. R. China

    Zhu Zheng-you

  3. Department of Mechanics, Shanghai University, 200436, Shanghai, P. R. China

    Cheng Chang-jun

  4. Shanghai Supercomputer Center, 201203, Shanghai, P. R. China

    Li Gen-guo

Authors
  1. Zhu Zheng-you
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  2. Li Gen-guo
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  3. Cheng Chang-jun
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Additional information

Contributed by Cupheng Chang-jun

Foundation items: the National Natural Science Foundation of China (60273048); the Science Foundation of Shanghai Municipal Commission of Education (99A01); the Science Foundation of Shanghai Municipal Commission of Sicences and Technology (98JC14032)

Biographies: Zuphu Zheng-you (1937-), Professor Lupi Gen-guo (1969-), Doctor

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Zheng-you, Z., Gen-guo, L. & Chang-jun, C. A numerical method for fractional integral with applications. Appl Math Mech 24, 373–384 (2003). https://doi.org/10.1007/BF02439616

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  • DOI: https://doi.org/10.1007/BF02439616

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