Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

Abstract

When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the error criterion of the least squares method, a quadratic programming method based on the frequency-domain error is proposed. In this method, the frequency-domain error minimization between the fractional operator s ± r and its rational approximation function is transformed into a quadratic programming problem. The results show that the construction method of the optimal rational approximation function of fractional calculus operator is effective, and the optimal rational approximation function constructed can effectively approximate the fractional calculus operator and model for the specified approximation frequency band.

Fractional Order Sliding Mode Controller for HBV Epidemic System

“…The definition of the integro-differential equation operator is presented in the study [64][65][66][67][68][69][70][71]:…”

“…The order  could be real or complex number. The upper and lower limit of operation are denoted by a and t. Three common definitions of fractional order derivative are presented as follows [64][65][66][67][68][69][70][71]: Riemann Louisville's definition…”