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Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system

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Abstract

The efficiency of the hardware implementations of fractional-order systems heavily relies on the efficiency of realizing the fractional-order derivative operator. In this work, a generic hardware implementation of the fractional-order derivative based on the Grünwald–Letnikov’s approximation is proposed and verified on a field-programmable gate array. The main advantage of this particular realization is its flexibility in applications which enable easy real-time configuration of the values of the fractional orders, step sizes, and/or other system parameters without changing the hardware architecture. Different approximation techniques are used to improve the hardware performance including piece-wise linear/quadratic methods. As an application, a variable-order chaotic oscillator is implemented and verified using fractional orders that vary in time.

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Acknowledgements

This work is supported by the System-On-Chip center at the Khalifa University of Science and Technology under Award No. (RC2-2018-020).

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Authors and Affiliations

  1. SoC Center, Khalifa University, P.O. Box 127788, Abu Dhabi, UAE

    Mohammed F. Tolba, Hani Saleh, Baker Mohammad & Mahmoud Al-Qutayri

  2. Department of Electrical and Computer Engineering, University of Sharjah, PO 27272, Sharjah, UAE

    Ahmed S. Elwakil

  3. Department of Electrical and Computer Engineering, University of Calgary, Alberta, Canada

    Ahmed S. Elwakil

  4. NISC Research Center, Nile University, Cairo, 12588, Egypt

    Ahmed S. Elwakil

  5. Department of Engineering Mathematics and Physics, Cairo University, Cairo, Egypt

    Ahmed G. Radwan

  6. NISC Research Center, Nile University, Cairo, 12588, Egypt

    Ahmed G. Radwan

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  1. Mohammed F. Tolba
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  2. Hani Saleh
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Correspondence to Baker Mohammad.

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Tolba, M.F., Saleh, H., Mohammad, B. et al. Enhanced FPGA realization of the fractional-order derivative and application to a variable-order chaotic system. Nonlinear Dyn 99, 3143–3154 (2020). https://doi.org/10.1007/s11071-019-05449-w

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