Affiliation:
1. Department of Computer Science, Czestochowa University of Technology, Dabrowskiego 73, 42-200 Czestochowa, Poland
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 presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented.
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