Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation
Mariusz Ciesielski
Abstract:Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is … Show more
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