A Note on Some Novel Laplace and Stieltjes Transforms Associated with the Relaxation Modulus of the Andrade Model

Abstract

In the framework of linear viscoelasticity, the authors have previously calculated a novel inverse Laplace transform involving the Mittag–Leffler function in order to calculate the relaxation modulus in the Andrade model. Here, we generalize this result, calculating the inverse Laplace transform of a given function Fα,βs by using two different approaches: the Bromwich integral and the decomposition of Fα,βs in simple fractions. From both calculations, we obtain a set of novel Laplace and Stieltjes transforms.

Keywords

• Laplace transform
• Stieltjes transform
• Mittag–Leffler function