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

Fractal and Fractional

Gerd Baumann¹ 

[1] Mathematics Department, German University in Cairo, New Cairo City, Egypt;

关键词: Sinc methods;    inverse Laplace transform;    indefinite integrals;    fractional calculus;    Mittag-Leffler function;    Prabhakar function;   

DOI  :  10.3390/fractalfract5020043

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown