Pseudo-Recursive Trapezoidal Rule for the Numerical Solution of Linear Fractional Differential Equations

This paper presents an extension of the trapezoidal integration rule, that in the present work is applied to devise a pseudo-recursive numerical algorithm for the numerical evaluation of fractional-order integrals. The main benefit of pseudo recursive implementation arises in terms of higher accuracy when the algorithm is run in the "short memory" version. The rule is suitably generalized in order to build a numerical solver for a class of fractional differential equations. The algorithm is also specialized to derive an efficient numerical algorithm for the on-line implementation of linear fractional order controllers. The accuracy of the method is theoretically analyzed and its effectiveness is illustrated by simulation examples.