FPGA Implementation of Special Functions used in Fractional Calculus
Synthesis and Analysis
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Fractional calculus deals with derivatives and integrals of arbitrary non-integer order. It is becoming very popular among the researchers in various fields as it is able to provide a more compact and realistic representation to many real-world and physical systems. The special mathematical functions like Mittag-Leffler function, Gamma and Dawson's function, etc., play a crucial role in the analysis of fractional-order systems and controllers. The response of any linear/nonlinear fractional-order system can be evaluated in terms of these special functions. The present text focuses on the hardw...
Fractional calculus deals with derivatives and integrals of arbitrary non-integer order. It is becoming very popular among the researchers in various fields as it is able to provide a more compact and realistic representation to many real-world and physical systems. The special mathematical functions like Mittag-Leffler function, Gamma and Dawson's function, etc., play a crucial role in the analysis of fractional-order systems and controllers. The response of any linear/nonlinear fractional-order system can be evaluated in terms of these special functions. The present text focuses on the hardware, especially FPGA, implementation of these special functions. A systematic step-by-step approach is presented for implementation of the special functions on FPGA platform. A thorough analysis of various implementation parameters like resource utilization, power consumption and operating frequency is also provided. The book is unique in the sense that it presents a methodological approach to real-time implementation of special functions in fractional calculus. The book will be a valuable resource to all researchers and students interested in hardware realization of fractional-order systems.
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