The purpose of this paper is to find approximate solutions the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). defined by Caputo derivative. A new form trial function from original presented and unknown coefficients in are computed LTCM. Two different initial-boundary value problems considered as test compared with analytical solutions. Numer...

In this paper, a Laplace homotopy analysis method which is based on homotopy analysis method and Laplace transform is applied to obtain the approximate solutions of fractional linear and non-linear differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives a high-order deformation equation in simple form. Numerical examples are includ...

In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltj...

This study proposes a novel computational technique for specific energy loss pulse incidence. Our method is based on fast inverse Laplace transform (FILT) with an electromagnetic field solver in the complex frequency domain. Using FILT algorithm, domain can be computed and transformed into time In our method, until desired observation without solving at previous time. The finite-difference comp...

For a skip-free Markov process on Z + with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.