A high-speed algorithm for computation of fractional differentiation and fractional integration | Zendy

Masataka Fukunaga | Zendy; Nobuyuki Shimizu | Zendy

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A high-speed algorithm for computation of fractional differentiation and fractional integration

Author(s) -

Masataka Fukunaga,

Nobuyuki Shimizu

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0152

Subject(s) - computation , function (biology) , fractional calculus , algorithm , mathematics , automatic differentiation , computer science , evolutionary biology , biology

A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as n log n, as opposed to n(2) of standard algorithms.

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