TY - JOUR A1 - Diethelm, Kai T1 - An Improvement of a Nonclassical Numerical Method for the Computation of Fractional Derivatives T2 - Journal of Vibration and Acoustics N2 - Standard methods for the numerical calculation of fractional derivatives can be slow and memory consuming due to the nonlocality of the differential operators. Yuan and Agrawal (2002, “A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives,” ASME J. Vibr. Acoust., 124, pp. 321–324) have proposed a more efficient approach for operators whose order is between 0 and 1 that differs substantially from the traditional concepts. It seems, however, that the accuracy of the results can be poor. We modify the approach, adapting it better to the properties of the problem, and show that this leads to a significantly improved quality. Our idea also works for operators of order greater than 1. KW - differential equations KW - numerical analysis KW - fractional derivative Y1 - 2009 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/2068 UR - https://nbn-resolving.org/urn:nbn:de:bvb:863-opus-20688 UR - https://asmedigitalcollection.asme.org/vibrationacoustics/article-abstract/131/1/014502/471073/An-Improvement-of-a-Nonclassical-Numerical-Method N1 - Accepted Version des Artikels. © ASME VL - 131 IS - 1 ER -