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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2012

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Numerical evaluation of fractional differ-integrals of some periodical functions via the IMT transformation

Brzeziński D., Ostalczyk P.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2012

Vol. 60, nr 2

285-292

This paper presents accuracy evaluation of the numerical calculations of the fractional differ-integrals. We focus on applying the Riemann-Liouville formula, on singularity, which appears while using classical form of this formula. To calculate it we use the Newton-Cotes’ Quadrature and additionally two Gaussian rules. Using this different approach to the IMT Transformation, transforming the “core” integrand of Riemann-Liouville formula, we point the possible way of increasing the accuracy of the calculations. We use our own tools and compare obtained results with, where possible, exact values, where not – values obtained using an excellent method of integration incorporated in Mathematica.