Closed-Form Rational Approximations of Fractional, Analog and Digital Differentiators/Integrators

摘要

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating $s^{nu}$, with $-1, and $(2/T)^{nu}((z-1)/(z+1))^{nu}$ . The expressions of the coefficients are given in terms of $nu$ and of the degree $n$ of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition.