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High Speed Algorithm for Computation of Fractional Differentiation and Integration

[+] Author Affiliations
Masataka Fukunaga

Nihon University, Sendai, Japan

Nobuyuki Shimizu

Iwaki Meisei University, Iwaki, Fukushima, Japan

Paper No. DETC2011-47408, pp. 169-178; 10 pages
doi:10.1115/DETC2011-47408
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME

abstract

A high speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm the stored data is not the history of the function to be differentiated or integrated but the history of the weighted integrals of the function. It is shown that, by the computational method based on the new algorithm, the integration time only increases in proportion to n log n, different from n2 by a standard method, for n steps of integrations of a differential integration.

Copyright © 2011 by ASME

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