The Fractional Complex Step Method | Zendy

Rabha W. Ibrahim | Zendy; Hamid A. Jalab | Zendy

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The Fractional Complex Step Method

Author(s) -

Rabha W. Ibrahim,

Hamid A. Jalab

Publication year - 2013

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2013/515973

Subject(s) - fractional calculus , operator (biology) , mathematics , differential operator , time scale calculus , stability (learning theory) , calculus (dental) , function (biology) , computer science , mathematical analysis , multivariable calculus , medicine , biochemistry , chemistry , dentistry , repressor , control engineering , machine learning , evolutionary biology , biology , transcription factor , engineering , gene

It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for computing the fractional order derivatives. Stability of the generalized fractional complex step approximations is demonstrated for an analytic test function

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