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<sup>ν</sup>, with , and (2/T)<sup>ν</sup>((z-1)/(z+1))<sup>ν</sup>. 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.

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