Abstract—Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed ...

We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R . Practically all previously proposed differential transformations of LPDOs are particular cases of this transformation (intertwining Laplace transformation, ILT ). We give a complete algorithm of construction of ILT and describe the classes of operators in...

In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented method for solving non-linear mathematical models. The numerical results for $N=5, 10$ are presented. Several $hbar$-c...

he development of algorithms needed for the analytic solution of state space design equations using a computer algebra system (MapleV) is presented in this article. These calculations involve mati ix manipulations, eigenvalue-eigenvector determinations, Laplace and Inverse Laplace transformations, Z and Inverse Z transformations, which are complex, tedious, and error prone, even for simple exam...