In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...

We consider a processor shared M/M/1 queue that can accommodate at most a finite number K of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K → ∞, by locating the dominant singularity of the Laplace transform. keywords: finite capacity, processor sharing, sojour...

In electrical engineering education exists a major difficulty for first level students, namely the Laplace transform. The question is: does this ubiquitous tool is needed in an electrical engineering course? Our answer is: Obviously, not. Based on an operational standpoint the paper describes some guidelines and results for a primer on handling signals and linear systems without using the Lapla...

In this study, the second type of Green and Naghdi's thermoelasticity theory is applied to present the vibration of a nanobeam subjected to rectified sine wave heating based upon the nonlocal thermoelasticity theory. Both Young's modulus and thermal conductivity are considered to be linear functions of the temperature. The Laplace transform domain is adopted to solve the governing partial diffe...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

We give an explicit formula (i.e., an explicit expression for the formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. Introduction We will denote by C((t)) (resp. C({t})) the field C[[t]][t] (resp. C{t}[t]) of formal (resp. convergent) Laurent series of the variable t, ...

The fundamental purpose of this paper is to propose a new Laplace-type integral transform (NL-TIT) for solving steady heat-transfer problems. proposed generalization the Sumudu, and Laplace transforms its visualization more comfortable than Sumudu transform, natural Elzaki transform. suggested used solve problems, results are compared with existing techniques.

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T ), covered by the process in the time interval [0, T ]. The Laplace transform of A(T ) follows as a consequence. The main proof involves a double Laplace transform of A(T ) and is based on excursion theory and local time for Browni...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

In the present paper we give a fractional generalization of the Lauwerier formulation of the boundary value problem of the temperature field in oil strata. The Caputo fractional derivative operator and the Laplace transform are the important tools for solving the proposed problem. By using Efros’ theorem which is a modified form of convolution theorem for Laplace transform, the solution is obta...