Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and Sinc-Gaussian based method. The two last Sinc related are exact transforms which allow us numerical approximation using methods. transform converges exponentially does not use Bromwich contours for computations. apply the to Mittag-Leffler functions incorporating one, two, parameters. parameter function represents Prabhakar’s function. used solve fractional differential equations constant variable differentiation order.