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

This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating s^ν, with , and (2/T)^ν((z-1)/(z+1))^ν. The expressions of the coefficients are given in terms of ν 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.