×

zbMATH — the first resource for mathematics

The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. (English) Zbl 1236.35003
Summary: The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order \(\alpha\), \(0<\alpha \leqslant 1\) are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of \(\alpha \) are shown graphically for some examples.

MSC:
35A25 Other special methods applied to PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adomian, G., J. math. anal. appl., 113, 202, (1986)
[2] Adomian, G., J. math. anal. appl., 124, 290, (1987)
[3] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston · Zbl 0802.65122
[4] Al-Khaled, K.; Momani, S., Appl. math. comput., 165, 2, 473, (2005)
[5] Caputo, M., Geophys. J. astr. soc., 13, 529, (1967)
[6] Diethelm, K.; Ford, N.J., Numer. anal. rep., 378, (2003)
[7] Diethelm, K.; Ford, N.J., Appl. math. comput., 154, 621, (2004)
[8] El-Sayed, A.M.A., Appl. math. comput., 49, 2-3, (1992)
[9] El-Sayed, A.M.A., Int. J. theor. phys., 35, 2, 311, (1996)
[10] Kaya, D., Int. J. comput. math., 75, 235, (2000)
[11] Lesnic, D., Appl. math. comput., 119, 197, (2001)
[12] Lesnic, D., Appl. math. lett., 15, 697, (2002)
[13] Lesnic, D., J. comput. appl. math., 147, 27, (2002)
[14] Momani, S., Phys. lett. A, 170, 2, 1126, (2005)
[15] Momani, S., Appl. math. comput., 165, 459, (2005)
[16] Momani, S.; Odibat, Z., Appl. math. comput., 177, 488, (2006)
[17] Momani, S.; Odibat, Z., Phys. lett. A, 335, 4-5, 271, (2006)
[18] I. Podlubny, A.M.A. El-Sayed, On Two Definitions of Fractional Calculus, Slovak Academy of Sciences Institute of Experimental Physics, ISBN 80-7099-250-2, 1996, UEF-03-96
[19] I. Podlubny, The Laplace Transform Method for Linear Differential Equations of Fractional Order, Slovak Academy of Sciences Institute of Experimental Physics, June, 1994, UEF-02-94
[20] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego · Zbl 0918.34010
[21] Podlubny, I., J. fract. calc., 5, 4, 367, (2002)
[22] Samko, S.; Kilbas, A.; Marichev, O., Fractional integrals and derivatives: theory and applications, (1993), Gordon and Breach London · Zbl 0818.26003
[23] Wazwaz, A.M., Chaos solitons fractals, 12, 12, 2283, (2001)
[24] Wazwaz, A.M., Appl. math. comput., 111, 53, (2000)
[25] Wazwaz, A.M., Appl. math. comput., 105, 11, (1999)
[26] Wyss, W., J. math. phys., 27, 2782, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.