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Comment on “FPGA realization of fractional order neuron”. (English) Zbl 1481.92025

Summary: This paper points out a number of mathematical inaccuracies in the recent paper [ibid. 81, 372–385 (2020; Zbl 1481.92027)] by S. A. Malik and A. H. Mir. The comments in this paper pertain mainly with the errors presented in Section 3 of that paper referencing the discretization of the fractional operator. Proposed corrections to the formulas and figures are presented along with a sample Maple code to verify the results.

MSC:

92C20 Neural biology
34A08 Fractional ordinary differential equations

Citations:

Zbl 1481.92027

Software:

Maple
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, Y. Q.; Moore, K. L., Discretization schemes for fractional-order differentiators and integrators, IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 49, 3, 363-367 (2002) · Zbl 1368.65035
[2] Two direct tustin discretization methods for fractional-order differentiator/integrator, J. Frankl. Inst., 340, 5, 349-362 (2003) · Zbl 1051.93031
[3] An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions, ISA Trans., 74, 229-238 (2018)
[4] Special Section: Fractional Calculus Applications in Signals and Systems · Zbl 1172.94364
[5] Malik, S.; Mir, A., Fpga realization of fractional order neuron, Appl. Math. Model., 81, 372-385 (2020) · Zbl 1481.92027
[6] Al-Alaoui, M. A., Filling the gap between the bilinear and the backward-difference transforms: an interactive design approach, Int. J. Electr. Eng. Educ., 34, 4, 331-337 (1997)
[7] Chen, Y.; Vinagre, B. M.; Podlubny, I., Continued fraction expansion approaches to discretizing fractional order derivatives an expository review, Nonlinear Dyn., 38, 1-4, 155-170 (2004) · Zbl 1134.93300
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