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.
- Design Engineering Division and Computers and Information in Engineering Division
High Speed Algorithm for Computation of Fractional Differentiation and Integration
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Fukunaga, M, & Shimizu, N. "High Speed Algorithm for Computation of Fractional Differentiation and Integration." Proceedings of the 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. pp. 169-178. ASME. https://doi.org/10.1115/DETC2011-47408
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