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A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains. (English) Zbl 1245.65141
Summary: A homotopy perturbation technique is proposed to solve a class of initial-boundary value problems of partial differential equations of arbitrary (fractional) orders over finite domains. The basic idea of this technique is to utilize both the initial and boundary conditions in the recursive relation of the solution scheme so that we can obtain a good approximate solution. Numerical examples are presented to illustrate the validity of the proposed technique.

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35R11 Fractional partial differential equations
Full Text: DOI
[1] He, J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. non-linear mech., 35, 1, 37-43, (2000) · Zbl 1068.74618
[2] He, J.H., Homotopy perturbation technique, Comput. math. appl. mech. eng., 178, 3-4, 257-262, (1999) · Zbl 0956.70017
[3] He, J.H., Some asymptotic methods for strongly nonlinear equations, Int. J. modern phys. B, 20, 1141-1199, (2006) · Zbl 1102.34039
[4] Lu, J.F., Analytical approach to Kawahara equation using variational iteration method and homotopy perturbation method, Topol. methods nonlinear anal. J. juliusz Schauder center, 32, 2, 287-294, (2008) · Zbl 1152.35091
[5] Lesnic, D., A computational algebraic investigation of the decomposition method for time-dependent problems, Appl. math. comput., 119, 97-206, (2001) · Zbl 1023.65107
[6] Lesnic, D., The decomposition method for forward and backward time-dependent problems, J. comput. appl. math., 147, 27-39, (2002) · Zbl 1013.65110
[7] Lesnic, D., The decomposition method for linear, one-dimensional, time-dependent partial differential equations, Int. J. math. math. sci., 2006, 1-29, (2006) · Zbl 1121.35004
[8] El-Sayed, A.M.A.; Gaber, M., The Adomian decomposition method for solving partial differential equations of fractal order in finite domains, Phys. lett. A, 359, 175-182, (2006) · Zbl 1236.35003
[9] Podlubny, I., Fractional differential equations, (1999), Academic Press San Diego · Zbl 0918.34010
[10] 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.
[11] El-Sayed, S.M., The decomposition method for studying the klein – gordon equation, Chaos solitons fract., 18, 1025-1030, (2001) · Zbl 1068.35069
[12] Kanth, A.R.; Aruna, K., Differential transform method for solving the linear nonlinear klein – gordon equation, Comput. phys. commun., 180, 708-711, (2009) · Zbl 1198.81038
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