Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract.2021, 5, 43.
Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract. 2021, 5, 43.
Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract.2021, 5, 43.
Baumann, G. Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus. Fractal Fract. 2021, 5, 43.
Abstract
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi-
mation, 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.
Computer Science and Mathematics, Applied Mathematics
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