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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 515973, 8 pages
Research Article

The Fractional Complex Step Method

1Institute of Mathematical Sciences, University of Malaya, 50603, Malaysia
2Faculty of Computer Science and Information Technology, University of Malaya, 50603, Malaysia

Received 24 January 2013; Revised 21 March 2013; Accepted 25 March 2013

Academic Editor: Jehad Alzabut

Copyright © 2013 Rabha W. Ibrahim and Hamid A. Jalab. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.