Two direct Tustin discretization methods for fractional-order differentiator/integrator

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given.