He used a similar transform on his additions to the probability theory. It became popular after World War Two. This transform was made popular by Oliver Heaviside, an English Electrical Engineer. Other famous scientists such as Niels Abel, Mathias Lerch, and Thomas Bromwich used it in the 19th...
bivariate Laplace transform order of residual livesThe Laplace transform order of residual life is viewed as a tool for the stochastic comparison of two life distributions. In this paper, we study new notions of stochastic comparisons based on the bivariate Laplace transform order of residual lives....
Find the Inverse Laplace Transform of (s^2 + s + 1) / ((s - 1)(s^2 + 4)) Find the inverse Laplace transform of F(s) = \frac{e^{-7s{s^2 + 4s - 5} f(t) = \boxed{\space} Find the inverse Laplace transform \mathcal{L}^{-1} \left\{\dfrac{1}{s^2} -...
But the integral in the right-hand term is the Laplace transform of the function, x(t), before it was shifted; that is, the right-hand integral is just L[x(t)]. Hence the Laplace transform of the shifted function becomes: (6.18)L[x(t−T)]=e−sTL[x(t)] Equation 6.18 is th...
Laplace transform is named in honor of Pierre-Simon Laplace, who used the transform in his work on probability theory, the transform was discovered originally by Leonhard Euler, the prolific eighteenth-centurySwissmathematician. The Laplace transform appears in all branches of mathematical physics - a...
In this study, we introduced the ψ -Laplace transform Adomian decomposition method, which is a combination of the efficient Adomian decomposition method with the generalization of the classical Laplace transform to treat fractional differential equations with respect to another function, ψ , ...
The problem of testing various classes of life distributions have been considered in the literature during the last decades. In this paper, we consider a new test statistic for testing exponentiality against used better than age (UBA) class of life distributions based on Laplace transform. This ...
In this article, we construct the series solution of the time-fractional Korteveg de Vries(K-dV) equation through a computational approach named as Laplace residual powerseries (LRPS) that combines the Laplace transform with the residual power series method(RPS). Time-fractional K-dV equation ...
The problem of testing various classes of life distributions have been considered in the literature during the last decades. In this paper, we consider a new test statistic for testing exponentiality against used better than age (UBA) class of life distributions based on Laplace transform. This...
double Laplace transformAdomian decomposition methodconformable fractional derivativeHerein,an approach known as conformable double Laplace decomposition method (CDLDM) is suggested for solving system of non-linear conformable fractional differential equations.The devised scheme is the combination of the ...