The variational iteration method for solving Riesz fractional partial differential equations

In this paper, the variational iteration method is applied to obtain the solution for space fractional partial differential equations where the space fractional derivative is in the Riesz sense. On the basis of the properties and definition of the fractional derivative, the iterative technique is carried out in a straightforward manner without the need for transforms or numerical approximations. Examples demonstrate that the series solution obtained shows agreement with the exact solutions of the problems solved.

[1]  G. Zaslavsky,et al.  Fractional dynamics of systems with long-range interaction , 2006, 1107.5436.

[2]  J. R. Leith,et al.  Fractal scaling of fractional diffusion processes , 2003, Signal Process..

[3]  A. A. Hemeda,et al.  Variational iteration method for solving wave equation , 2008, Comput. Math. Appl..

[4]  Mariusz Ciesielski,et al.  Numerical treatment of an initial-boundary value problem for fractional partial differential equations , 2006, Signal Process..

[5]  S. Das,et al.  Analytical solution of a fractional diffusion equation by variational iteration method , 2009, Comput. Math. Appl..

[6]  Fawang Liu,et al.  Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation , 2009, Appl. Math. Comput..

[7]  The Fundamental Solutions of the Space, Space-Time Riesz Fractional Partial Differential Equations with Periodic Conditions , 2007 .

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

[9]  Y. Fung,et al.  Variational Methods in the Mechanics of Solids , 1982 .

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

[11]  Mohd. Salmi Md. Noorani,et al.  Variational iteration method for fractional heat- and wave-like equations , 2009 .

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

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

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

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

[16]  R. Gorenflo,et al.  Discrete random walk models for space-time fractional diffusion , 2002, cond-mat/0702072.

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

[18]  Qian Guo,et al.  An iteration formulation for normalized diode characteristics: Letters to the Editor , 2004 .

[19]  I. Turner,et al.  Numerical methods for fractional partial differential equations with Riesz space fractional derivatives , 2010 .

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

[21]  Rudolf Gorenflo,et al.  Fully discrete random walks for space-time fractional diffusion equations , 2003, Signal Process..