IJPAM: Volume 109, No. 3 (2016)
TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
Department of Physics
Bu-Ali Sina University
Department of Electrical Engineering
Bu-Ali Sina University
Abstract. This paper presents a general solitary solution of a class of nonlinear time-fractional partial differential equations by Adomian decomposition method(ADM). This class of nonlinear time-fractional partial differential equations include a lot of standard nonlinear partial differential equations in mathematical physics. The solitary solution obtained by ADM is a general solitary solution and admit you investigate the solution for different initial conditions and different ( is the order of derivative respect to time ). Also the solution subject to the especial initial conditions and reduce to the solution of standard partial differential equation. Additionally, it use the fractional derivative of Caputo sense.
Received: April 13, 2016
Revised: July 19, 2016
Published: October 1, 2016
AMS Subject Classification: 34A08, 76B25, 65M55
Key Words and Phrases: fractional differential equation, solitary wave, Adomian decomposition method
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- Ji-Huan He, Xu-Hong Wu, Constraction of solitary solution andcompacton-like solution by variational iteration method. Chaos,Soliton and Fractals, 29, (2006), 108-113.
- M. Inc, The approximate and exact solutions of the space and timefractional Burgers equations with initial conditions by variationaliteration method. J. Math. Anal. Appl., 345, (2008),476-484.
- W. Malfiet, W., Hereman, The Tanh Method: I. Exact solutions ofnonlinear evolution and wave equations. Phys Scr., 54,(1996), 563-568.
- W. Malfiet, W., Hereman, The Tanh Method: II. Perturbation Techniquefor Conservative Systems. Phys Scr. 54, (1996), 569-575.
- Z. M. Odibat, Exact solitary solutions for variants of the KdVeqations with fractional time derivatives. Chaos, Soliton andFractals 40, (2009), 1264-1270.
- H. Parsian, Time Fractional Wave Equation: Caputo Sense. Adv.Studies Theor. Phys. Vol. 6, no. 2(2012), 95-100.
- S. Z. Rida, H. M. El-Sherbinyb, A. A. M. Arafa, On the solution ofthe fractional nonlinear Schrodinger equation. Phys. letters A372, (2008), 553-558.
- M. Wadati, Introduction to soliton. Pramana- J Phys (2001).
- A. M. Wazwaz, A new algorithm for calculating adomian polynomialsfor nonlinear operators. Appli. Math. Comput. 111,(2000), 33-51.
DOI: 10.12732/ijpam.v109i3.22 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 757 - 762