Accuracy Assessment of Fractional Order Derivatives and Integrals Numerical Computations - Brzeziński, Dariusz W.; Ostalczyk, P. (Journal of Applied Nonlinear Dynamics, 2026)
This paper presents results of a numerical experiment, during which different numerical criteria of exact values setting in the accuracy assessment of fractional order derivatives / integrals numerical calculations are tested. Although traditional accuracy criteria in form of relative error expressed in % are applied, the values assumed as exact, necessary for comparison, are now: value of a function, classical 1st derivative, integral of the 1st order and Mittag-Leffler function’s values. For that purpose, fractional order differentiation and integration operators concatenation rules are applied. The methods allow to assess the accuracy of numerical calculations of fractional derivatives and integrals for each required function and not only for ones, for which mathematical formulas are available. The proposed measures are employed to determine proper operation and assess the accuracy of fractional order derivatives and integrals numerical algorithms.The algorithms utilize Riemann-Liouville and Grunwald-Letnikov frac-¨ tional order derivatives and integrals formulas.