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

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.