Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions
By Mehdi Dehghan, Jalil Manafian, Abbas Saadatmandi. 2010
141 citations recorded by the source corpus.
In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.
Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/445bbb82e3a86f9074f0d8e7747858ec05301b1a
How researchers see this paper
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In Modeling and Simulation
- Mehdi Dehghan
- Mehrdad Lakestani
- S. Yousefi
- Ali Lotfi
- S. Irandoust‐pakchin
- Ali H. Bhrawy
- Yadollah Ordokhani
- Abbas Saadatmandi
In Numerical Analysis
- Mehrdad Lakestani
- Ali Lotfi
- S. Yousefi
- Mehdi Dehghan
- S. Irandoust‐pakchin
- Ali Shokri
- Ali H. Bhrawy
- Abbas Saadatmandi
In Statistical and Nonlinear Physics
- Mehrdad Lakestani
- S. Yousefi
- Ali Lotfi
- Mehdi Dehghan
- Jalil Manafian
- Ali Shokri
- Abdul-Majid Wazwaz
- Abbas Saadatmandi
Citations in the corpus
- THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, background): “We also refer the interested reader to [6,7,10,13,18,19,25,37,38,45].”
- The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems (2011, methodology): “We refer the interested reader to Dehghan and Shakeri (2008), Dehghan et al. (2009), Dehghan and Salehi (2010), Dehghan and Shakeri (2010), Dehghan et al. (2010) for employing some alternative approaches based on the semi-analytical techniques.”