Charef rational approximation of fractional operators and singular properties of novel scale equations

Abstract:

According to the single-fraction power pole and zero model of the Charef rational approximation of the fraction operator, two new types of non-normal scaling equations-the novel scaling equation are introduced, which are used to characterize the limit cases of the Charef rational approximation of the fraction operator. It is physically realizable. Firstly, we investigate the operational validity and performance of the rational function sequence of the novel scale equation, and compare the difference with the typical scale equation. It is found that the real solution of the rational function sequence of the novel scale equation is different from the approximate solution. This equation provides a new idea for the approximate solution of the scale equation. Then combined with the localization feature of the zero-pole subsystem, the operation oscillation period of the novel scaling equation is quantitatively analyzed. Finally, it is found that the distribution of poles and zeros in the complex plane is different from the typical scaling equation, and the singular characteristics of the novel scaling equation are found.