%0 Journal Article
%T A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations
%A Fatima A. Alawad
%A Eltayeb A. Yousif
%A Arbab I. Arbab
%J International Journal of Differential Equations
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/256593
%X In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders. 1. Introduction Fractional differential equations are widely used in many branches of sciences. Many phenomena in engineering, physics, chemistry and other sciences can be described successfully using fractional calculus. Nonlinear oscillation of earthquake, acoustics, electromagnetism, electrochemistry, diffusion processes and signal processing can be modeled by fractional equations [1¨C5]. The telegraph equations have a wide variety of application in physics and engineering. The applications arise, for example, in the propagation of electrical signals and optimization of guided communication systems [6¨C9]. It is recently shown by Arbab [10] that a quaternionic momentum eigenvalue produces a telegraph equation. This equation is found to describe the propagation of a quantum particle. The fractional telegraph equations have been investigated by many authors in recent years. Garg et al. [9] derived a solution of space-time fractional telegraph function in a bounded domain by the method of generalized differential transform and obtained the solution in terms of Mittage-Leffler functions. Chen et al. [11] obtained the solution of nonhomogenous time-fractional telegraph equation with nonhomogenous boundary conditions, namely, Dirichlet, Neumann, and Robin boundary conditions using the method of separation of variables. The solutions are given in the form of the multivariate Mittage-Leffler functions. Ansari [12] derived a formal solution of the time-fractional telegraph equation by applying a fractional exponential operator. Huang [13] considered the time-fractional telegraph equation for the Cauchy problem and signaling problem. He solved the problem by the combined Fourier-Laplace transforms. Also, Huang derived the solution for the bounded problem in a bounded-space domain by means of Sine-Laplace transforms methods. Das et al. [14] used a homotopy analysis method in approximating an analytical solution for the time-fractional telegraph equation and different particular cases have been derived. Jiang and Lin [15] obtained the solution in a series form for the time-fractional telegraph equation with Robin boundary value conditions
%U http://www.hindawi.com/journals/ijde/2013/256593/