Numerical scheme for calculating of the fractional two-power relaxation laws in time-domain of measurements

A numerical approximation of the three-parameter Mittag-Leffler function, useful for description of the non-exponential relaxation laws, is presented. Our approach is based on the Dirichlet average of the two-parameter Mittag-Leffler function for which the numerical approximation is well developed. We provide estimates for accuracy of the computation.

► Proposed a new method for computing the three-parameter Mittag-Leffler function.
► Based on a singular quadrature of the two-parameter Mittag-Leffler function.
► Applied for real and complex arguments.
► Estimated errors.
► Considered some examples from the theory of relaxation.