Variational iteration method for fractional heat- and wave-like equations

This paper applies the variational iteration method to obtaining analytical solutions of fractional heat- and wave-like equations with variable coefficients. Comparison with the Adomian decomposition method shows that the VIM is a powerful method for the solution of linear and nonlinear fractional differential equations.

[1]  Ralf Metzler,et al.  Boundary value problems for fractional diffusion equations , 2000 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  Jafar Biazar,et al.  He's Variational Iteration Method for Solving Hyperbolic Differential Equations , 2007 .

[4]  Shaher Momani,et al.  Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method , 2005, Appl. Math. Comput..

[5]  Mohd. Salmi Md. Noorani,et al.  Application of variational iteration method to heat- and wave-like equations , 2007 .

[6]  A. Hanyga,et al.  Multi–dimensional solutions of space–time–fractional diffusion equations , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  Shaher Momani,et al.  Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations , 2007, Comput. Math. Appl..

[8]  Ji-Huan He.  A new approach to nonlinear partial differential equations , 1997 .

[9]  Joseph Klafter,et al.  Fractal behavior in trapping and reaction: A random walk study , 1984 .

[10]  A. Wazwaz.  A study on linear and nonlinear Schrodinger equations by the variational iteration method , 2008 .

[11]  S. Momani,et al.  Numerical comparison of methods for solving linear differential equations of fractional order , 2007 .

[12]  S. Momani,et al.  Analytical approach to linear fractional partial differential equations arising in fluid mechanics , 2006 .

[13]  Francesco Mainardi,et al.  Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[14]  G. Drăgănescu,et al.  Application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives , 2006 .

[15]  S. Momani,et al.  Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order , 2008 .

[16]  Shaher Momani,et al.  Application of He’s variational iteration method to Helmholtz equation , 2006 .

[17]  O. Agrawal.  Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain , 2002 .

[18]  Mohd. Salmi Md. Noorani,et al.  The multistage variational iteration method for a class of nonlinear system of ODEs , 2007 .

[19]  N. Sweilam,et al.  Numerical studies for a multi-order fractional differential equation , 2007 .

[20]  Davood Domiri Ganji,et al.  Solution of the Generalized Nonlinear Boussinesq Equation Using Homotopy Perturbation and Variational Iteration Methods , 2007 .

[21]  Ji-Huan He,et al.  Beyond Adomian method: The variational iteration method for solving heat-like and wave-like equations with variable coefficients , 2008 .

[22]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[23]  Shaher Momani,et al.  Numerical solution of Fokker–Planck equation with space- and time-fractional derivatives , 2007 .

[24]  R. Gorenflo,et al.  Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.

[25]  Prince Abdullah bin Ghazi,et al.  Modified homotopy perturbation method : Application to quadratic Riccati differential equation of fractional order , 2007 .

[26]  Shaher Momani,et al.  Numerical approach to differential equations of fractional order , 2007 .

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

[28]  H. Sekine,et al.  General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics1 , 1980 .

[29]  Necdet Bildik,et al.  The Use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations , 2006 .

[30]  Yongguang Yu,et al.  The synchronization of fractional-order Rössler hyperchaotic systems☆ , 2008 .

[31]  Asghar Ghorbani,et al.  He's Homotopy Perturbation Method for Calculating Adomian Polynomials , 2007 .

[32]  A. A. Soliman,et al.  A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations , 2006 .

[33]  Ahmed Alawneh,et al.  Variational iteration method for solving the space‐ and time‐fractional KdV equation , 2008 .

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

[35]  Ji-Huan He.  Variational iteration method – a kind of non-linear analytical technique: some examples , 1999 .

[36]  Ji-Huan He.  Approximate solution of nonlinear differential equations with convolution product nonlinearities , 1998 .

[37]  Ji-Huan He,et al.  Variational iteration method for delay differential equations , 1997 .

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

[39]  Ji-Huan He,et al.  An iteration formulation for normalized diode characteristics , 2004, Int. J. Circuit Theory Appl..

[40]  Hang Xu,et al.  Analysis of a time fractional wave-like equation with the homotopy analysis method , 2008 .

[41]  Nabil T. Shawagfeh,et al.  Analytical approximate solutions for nonlinear fractional differential equations , 2002, Appl. Math. Comput..

[42]  P. Ruján,et al.  Continuous kink condensation in the planar quantum hamiltonian , 1979 .

[43]  E. Yusufoglu,et al.  Variational Iteration Method for Construction of Some Compact and Noncompact Structures of Klein-Gordon Equations , 2007 .