NUMERICAL APPROXIMATION OF THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS USING THE AKIMA SPLINE INTERPOLATION

This paper presents the numerical algorithms for evaluating the values of the left-and right-sided Riemann-Liouville fractional integrals using the linear and Akima cubic spline interpolations. Sample numerical calculations have been performed based on the derived algorithms. The results are presented in two tables. Knowledge of the closed analytical expressions for sample fractional integrals makes it possible to determine the numerical errors and the experimental rates of convergence for each derived algorithm.