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Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition. (English) Zbl 1102.65135
Summary: The Adomian decomposition method is used to obtain solutions of linear/nonlinear fractional diffusion and wave equations. Some illustrative examples are presented.

MSC:
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals
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[1] Abboui, K.; Cherruault, Y., New ideas for proving convergence of decomposition methods, Comput. appl. math., 29, 7, 103-105, (1995) · Zbl 0832.47051
[2] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer · Zbl 0802.65122
[3] Babolian, E.; Biazar, J.; Vahidi, A.R., The decomposition method applied to systems of Fredholm integral equations of the second kind, Appl. math. comput., 148, 2, 443-452, (2004) · Zbl 1042.65104
[4] Biazar, J.; Babolian, E.; Islam, R., Solution of Volterra integral equations of the first kind by Adomian method, Appl. math. comput., 139, 249-258, (2003) · Zbl 1027.65180
[5] Biazar, J.; Babolian, E.; Islam, R., Solution of ordinary differential equations by Adomian decomposition method, Appl. math. comput., 147, 3, 713-719, (2004) · Zbl 1034.65053
[6] Biazar, J.; Islam, R., Solution of wave equation by Adomian decomposition method and the restrictions of the method, Appl. math. comput., 149, 3, 807-814, (2004) · Zbl 1038.65100
[7] Daftardar-Gejji, V.; Jafari, H., Adomian decomposition: a tool for solving a system of fractional differential equations, J. math. anal. appl., 301, 2, 508-518, (2005) · Zbl 1061.34003
[8] Diethelm, K., An algorithm for the numerical solution of differential equations of fractional order, Electron. trans. numer. anal., 5, 1-6, (1997) · Zbl 0890.65071
[9] El-Sayed, A.M.A., Fractional-order diffusion-wave equation, Int. J. theor. phys., 35, 2, 311-322, (1996) · Zbl 0846.35001
[10] Kaya, D.; El-Sayed, S.M., A numerical solution of the klein – gordon equation and convergence of the decomposition method, Appl. math. comput., 156, 2, 341-353, (2004) · Zbl 1084.65101
[11] Luchko, Yu.; Gorenflo, R., An operational method for solving fractional differential equations with the Caputo derivatives, Acta math vietnamica, 24, 2, 207-233, (1999) · Zbl 0931.44003
[12] Mainardi, F., On the initial value problem for the fractional diffusion-wave equation, (), 246-251
[13] Mainardi, F., Fundamental solutions for the fractional diffusion-wave equation, Appl. math. lett., 9, 23-28, (1996) · Zbl 0879.35036
[14] Moustafa, O.L., On the Cauchy problem for some fractional order partial differential equations, Chaos, soltions fractals, 18, 135-140, (2003) · Zbl 1059.35034
[15] Nigmatullin, R.R., The realization of the generalized transfer equation in a medium with fractal geometry, Phys. status solidi B, 133, 425, (1986)
[16] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego · Zbl 0918.34010
[17] Samko, G.; Kilbas, A.A.; Marichev, O.I., Fractional integrals and derivatives: theory and applications, (1993), Gordon and Breach Yverdon · Zbl 0818.26003
[18] Schneider, W.R.; Wyss, W., J. math. phys., 30, 1, 134-144, (1998)
[19] Shawaghfeh, N.T., Analytical approximate solutions for nonlinear fractional differential equations, Appl. math. comput., 131, 517-529, (2002) · Zbl 1029.34003
[20] Wazwaz, A.M., A reliable technique for solving the wave equation in infinite one-dimensional medium, Appl. math. comput., 92, 1-7, (1998) · Zbl 0942.65107
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