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


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. © 2020, Springer Nature B.V.


Tolba M.F., Saleh H., Mohammad B., Al-Qutayri M., Elwakil A.S., Radwan A.G.


Chaotic oscillators; FPGA; Fractional-order systems

Document Type



Nonlinear Dynamics, Vol. 99, PP. 3143 to 3154, Doi: 10.1007/s11071-019-05449-w

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