An Approximation to Solution of Space and Time Fractional Telegraph Equations by He′s Variational Iteration Method

Abstract

He's variational iteration method (VIM) is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

“…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][7][8][9]. It is recently shown by Arbab [10] that a quaternionic momentum eigenvalue produces a telegraph equation.…”

“…They considered fractional Taylor series and fractional initial conditions in deriving the solution. Sevimlican [6] considered a one-dimensional space fractional telegraph equations by the variation iteration method; he found the general Lagrange multiplier to be = ( − ). But, as mentioned by He [17] the exact identification of the general Lagrange multiplier is impossible for most problems and an approximate identification is always followed.…”

Fractional Difference Approximations for Time-Fractional Telegraph Equation

“…Actually, some authors have already studied the numerical solutions to some kinds of time or space fractional telegraph equations, such as C. Li [14], Z. Zhao [15], N. J. Ford [16], A. Sevimlican [17], and M. Dehghan [18]. The fractional telegraph equation we consider here is different from all of which they discussed in their papers.…”

Reduction of Some Fractional Partial Differential Equations with Variable Coefficients and Exact Solutions

“…This may be due to the fact that in these later systems evolution equations are nonlinear or semilinear and they are of higher order derivatives. The relevant studies are mainly focusing on the numerical treatment to these equations [9][10][11]. It had been pointed out that anomalous diffusion and anomalous transport, as novel phenomena do occur [1][2][3][4][5][6].…”