Abstract. A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function...

In this paper, approximate analytical solution of SIRC model associated with the evolution of influenza A disease in human population is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and padé approximant. The MDTM is used to increase the a...

although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

From the main equation (ax2 + bx + c)y′′ n (x) + (dx + e)y′ n(x)− n((n− 1)a+ d)yn(x) = 0, n∈ Z+, six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x = pz−1 + q, p = 0, q ∈ R. Some new int...

All methods presented in textbooks for computing inverse -transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence whose -transform is ; 2) computation using the inversion integral method becomes labored when has poles at the origin of the complex plane; 3...

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.