He's homotopy perturbation method for solving the space- and time-fractional telegraph equations

In this study, homotopy perturbation method (HPM) is used to obtain analytic and approximate solutions of the space- and time-fractional telegraph equations. The space- and time-fractional derivatives are considered in the Caputo sense. The analytic solutions are calculated in the form of a series with easily computable terms. Some examples are given. The results reveal that HPM is very effective and convenient.

[1]  Ahmet Yildirim,et al.  Application of the homotopy perturbation method for the Fokker–Planck equation , 2010 .

[2]  Subir Das,et al.  Solution of Fractional Vibration Equation by the Variational Iteration Method and Modified Decomposition Method , 2008 .

[3]  Ahmet Yildirim,et al.  He's homotopy perturbation method for nonlinear differential-difference equations , 2010, Int. J. Comput. Math..

[4]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[5]  Mehdi Dehghan,et al.  Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method , 2007 .

[6]  Mehdi Dehghan,et al.  Numerical solution of the Klein–Gordon equation via He’s variational iteration method , 2007 .

[7]  Mehdi Dehghan,et al.  Solution of delay differential equations via a homotopy perturbation method , 2008, Math. Comput. Model..

[8]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[9]  Ahmet Yildirim,et al.  Determination of periodic solution for a u1/3 force by He's modified Lindstedt–Poincaré method , 2007 .

[10]  Mehdi Dehghan,et al.  On the convergence of He's variational iteration method , 2007 .

[11]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[12]  A Yildirim,et al.  THE HOMOTOPY PERTURBATION METHOD FOR APPROXIMATE SOLUTION OF THE MODIFIED KDV EQUATION , 2008 .

[13]  Ahmet Yildirim,et al.  Solutions of singular IVPs of Lane–Emden type by homotopy perturbation method , 2007 .

[14]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[15]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[16]  Ahmet Yildirim,et al.  Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method , 2008, Comput. Math. Appl..

[17]  Mehdi Dehghan,et al.  SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD , 2008 .

[18]  Ahmet Yildirim,et al.  A Comparative Study of He's Homotopy Perturbation Method for Determining Frequency-amplitude Relation of a Nonlinear Oscillator with Discontinuities , 2007 .

[19]  Hossein Jafari,et al.  Application of the homotopy perturbation method to coupled system of partial differential equations with time fractional derivatives , 2008 .

[20]  Ahmet Yildirim,et al.  A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity , 2007 .

[21]  Mehdi Dehghan,et al.  Inverse problem of diffusion equation by He's homotopy perturbation method , 2007 .

[22]  Shaher Momani,et al.  Applications of variational iteration and homotopy perturbation methods to fractional evolution equations , 2008 .

[23]  Ji-Huan He,et al.  Exp-function method for nonlinear wave equations , 2006 .

[24]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[25]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[26]  Shaher Momani,et al.  Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods , 2008 .

[27]  M. Caputo.  Linear models of dissipation whose Q is almost frequency independent , 1966 .

[28]  L. Beghin,et al.  Time-fractional telegraph equations and telegraph processes with brownian time , 2004 .

[29]  Shaher Momani,et al.  Homotopy perturbation method for nonlinear partial differential equations of fractional order , 2007 .

[30]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[31]  Mehdi Dehghan,et al.  USE OF HES HOMOTOPY PERTURBATION METHOD FOR SOLVING A PARTIAL DIFFERENTIAL EQUATION ARISING IN MODELING OF FLOW IN POROUS MEDIA , 2008 .

[32]  Mehdi Dehghan,et al.  A numerical method for solving the hyperbolic telegraph equation , 2008 .

[33]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[34]  Ji-Huan He.  Homotopy Perturbation Method for Bifurcation of Nonlinear Problems , 2005 .

[35]  Galip Oturanç,et al.  A new analytical approximate method for the solution of fractional differential equations , 2008, Int. J. Comput. Math..

[36]  Ji-Huan He.  AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[37]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[38]  Ahmet Yildirim,et al.  The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation , 2008 .

[39]  M. Dehghan,et al.  Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems , 2009 .

[40]  Ji-Huan He.  Approximate analytical solution for seepage flow with fractional derivatives in porous media , 1998 .

[41]  Ji-Huan He,et al.  Recent development of the homotopy perturbation method , 2008 .

[42]  Mehdi Dehghan,et al.  Solving a fourth‐order fractional diffusion‐wave equation in a bounded domain by decomposition method , 2008 .

[43]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[44]  Enzo Orsingher,et al.  THE SPACE-FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS , 2003 .

[45]  Ji-Huan He.  New interpretation of homotopy perturbation method , 2006 .

[46]  Ahmet Yildirim,et al.  Traveling Wave Solution of Korteweg-de Vries Equation using He's Homotopy Perturbation Method , 2007 .

[47]  S. Momani,et al.  Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .

[48]  Mehdi Dehghan,et al.  Solution of parabolic integro‐differential equations arising in heat conduction in materials with memory via He's variational iteration technique , 2010 .

[49]  Shaher Momani,et al.  Analytic and approximate solutions of the space- and time-fractional telegraph equations , 2005, Appl. Math. Comput..

[50]  Ji-Huan He.  HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .