Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition

Adomian decomposition method has been used to obtain solutions of linear/nonlinear fractional diffusion and wave equations. Some illustrative examples have been presented.

[1]  R. Gorenflo,et al.  AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES , 1999 .

[2]  Y. Cherruault,et al.  New ideas for proving convergence of decomposition methods , 1995 .

[3]  W. Schneider,et al.  Fractional diffusion and wave equations , 1989 .

[4]  Abdul-Majid Wazwaz A reliable technique for solving the wave equation in an infinite one-dimensional medium , 1998, Appl. Math. Comput..

[5]  R. Nigmatullin The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry , 1986, January 1.

[6]  Salah M. El-Sayed,et al.  A numerical solution of the Klein-Gordon equation and convergence of the decomposition method , 2004, Appl. Math. Comput..

[7]  Roberto Monaco,et al.  Waves and Stability in Continuous Media , 1991 .

[8]  F. Mainardi The fundamental solutions for the fractional diffusion-wave equation , 1996 .

[9]  Hossein Jafari,et al.  Adomian decomposition: a tool for solving a system of fractional differential equations , 2005 .

[10]  Jafar Biazar,et al.  Solution of wave equation by Adomian decomposition method and the restrictions of the method , 2004, Appl. Math. Comput..

[11]  Jafar Biazar,et al.  Solution of the system of ordinary differential equations by Adomian decomposition method , 2004, Appl. Math. Comput..

[12]  Jafar Biazar,et al.  Solution of a system of Volterra integral equations of the first kind by Adomian method , 2003, Appl. Math. Comput..

[13]  A. El-Sayed,et al.  Fractional-order diffusion-wave equation , 1996 .

[14]  Jafar Biazar,et al.  The decomposition method applied to systems of Fredholm integral equations of the second kind , 2004, Appl. Math. Comput..

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

[16]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[17]  Osama L. Moustafa,et al.  On the Cauchy problem for some fractional order partial differential equations , 2003 .

[18]  K. Diethelm AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .

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

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