This paper proposes FPGA realization of an IP core for generic fractional-order derivative based on Grünwald-Letnikov approximation. This generic design is applied to achieve reconfigurable realization of fractional-order chaotic systems. The fractional-order real-time configuration boosts the suitability of this particular realization for different applications, including dynamic switching, synchronization, and encryption. The proposed design targets optimized utilization of the FPGA internal resources and efficient employment of the external peripherals: switches and I/O ports in the FPGA board. The digital design of the fractional-order dependent terms: binomial coefficients and power function is proposed. Three approximations of the power function using curve fitting are compared, settling on the quadratic approximation that balances accuracy and efficiency. Three fractional-order chaotic systems: Liu, Li and Chen four-wing, are verified for both commensurate and incommensurate orders cases, using one approach for the commensurate order case and two approaches for the incommensurate order case. The reconfigurable design is realized on the Artix-7 FPGA board, yielding throughputs of 1.1266, 1.1266, and 1.434 Gbit/s for both commensurate and incommensurate orders cases of the three systems, respectively. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications. © 2013 IEEE.
Mohamed S.M., Sayed W.S., Said L.A., Radwan A.G.
FPGA; fractional calculus; fractional-order chaotic systems; Grünwald-Letnikov
IEEE Access, Vol. 9, Art. No. 9458255, PP. 89376 to 89389, Doi: 10.1109/ACCESS.2021.3090336