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

Abstract

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.

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

“…which agrees with the solution already obtained in [18]. If we take = 2 then we get the exact solution of standard telegraph equation:…”

“…Khan et al [15], Kumar et al [16], and Prakash [17] applied a combination of single Laplace transform and homotopy perturbation method to obtain analytic and approximate solutions of the spacetime fractional telegraph equations. Alawad et al [18] used a combination of single Laplace transform and variational iteration method for finding exact solutions of space-time fractional telegraph equations in terms of Mittag-Leffler functions. Kumar in [19] coupled single Laplace transform and homotopy analysis method for the solution of spacefractional telegraph equation.…”

Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method

“…The telegraph equation describes the signal propagation of an electrical signal in transmission cable lines in general. Recently, many researchers and engineers have done excellent work to solve the fractional telegraph equation by different methods, such as the Laplace transform method [2], Laplace transform variational iteration method [3], double Laplace transform method [4], variational iteration method [5], Adomian decomposition method [6], Mixture of a new integral transform and homotopy perturbation method (HPM) [7], homotopy analysis method (HAM) [8], Chebyshev tau method [9], and the method of separating variables [10]. The natural transform Adomian decomposition method (NTDM) is a combination of the natural transform method and Adomian decomposition method.…”

A Modified Fractional Differential Love Model

“…The theory of the study was first constrained to the field of pure theoretical mathematics three centuries ago which is beneficial to both the theoretical physicists and mathematicians only [8] . Also, it had been successfully used in modeling many physical phenomena these days together with nonlinear oscillation of earthquake, acoustics, electromagnetism, electrochemistry, diffusion system, fluid float, polymer physics, mathematical biology and numerous regions of technological know-how [1] , [9]. The study is a micro experiment whereby small sample size was determined according to specified model.…”