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

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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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 (2020). https://doi.org/10.1007/s11071-019-05449-w

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Keywords

  • Fractional-order systems
  • Chaotic oscillators
  • FPGA