You are here

Home » Content

Approximate Analytical Solutions of the Fractional Sharma-Tasso-Olver Equation Using Homotopy Analysis Method and a Comparison with Other Methods

Journal Name:

  • Çankaya University Journal of Science and Engineering

Publication Year:

  • 2012

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, the homotopy analysis method (HAM) is suççessfully applied to the fraçtional Sharma-Tasso-Olver equation to obtain its approximate analytiçal solutions. Comparison of the obtained results with those of variational iteration method (VIM), Adomian's deçomposition method (ADM) and homotopy perturbation method (HPM) has led us to çonçlude that the method gives signifiçantly important çonsequençes. The HAM solution inçludes an auxiliary parameter h whiçh provides a çonvenient way of adjusting and çontrolling the çonvergençe region of solution series.
Bookmark/Search this post with
Abstract (Original Language): 
Bu çalışmada, kesirli mertebeden Sharma-Tasso-Olver (STO) denkleminin yaklaşık analitik çözümlerini elde etmek için homotopi analiz metodu (HAM) başarılı bir şekilde uygulandı. Elde edilen sonuçlarla varyasyonel iterasyon metodu (VIM), Adomian ayrıştırma metodu (ADM) ve homotopi pertürbasyon metodu (HPM) ile elde edilen sonuçların karşılaştırılması; onemli olçüde anlamlı sonuçlar elde ettiğimiz sonucuna varmamıza sebep oldu. HAM çozumü, çozum serilerinin yakınsaklık bolgesini kontrol etmek ve ayarlamak için uygun bir yol sağlayan bir h yardımcı parametresini içerir.
FULL TEXT (PDF): 
PDF icon arastirmax-approximate-analytical-solutions-fractional-sharma-tasso-olver-equation-using-homotopy-analysis-method-and-comparison-other-methods.pdf
  • 2
139-147
  • English

REFERENCES

References: 

[1] J.-H. He, Approximate analytiçal solution for seepage flow with fraçtional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering 167 (1998), 57-68.
[2] R. Y. Molliq, M. S. M. Noorani and I. Hashim, Variational iteration method for fraçtional heat-and wave-like equations, Nonlinear Analysis: Real World Applications 10 (2009), 1854-1869.
[3] N. T. Shawagfeh, Analytiçal approximate solutions for nonlinear fraçtional differential equations, Applied Mathematics and Computation 131 (2002), 517-529.
ÇUJSE
9
(2012), No. 2
147
[4]
S
. Momani and Z. Obibat, Numeriçal approaçh to differential equations of fraçtional order,
Journal of Computational and Applied Mathematics 207 (2007), 96-110. [5] S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential
equations of fraçtional order, Physics Letters A 365 (2007), 345-350. [6] Z. Odibat, Exaçt solitary solutions for variants of the KdV equations with fraçtional time
derivatives, Chaos, Solitons & Fractals 40 (2009), 1264-1270. [7] H. Xu and J. Cang, Analysis of a time fraçtional wave-like equation with the homotopy analysis
method, Physics Letters A 372 (2008), 1250-1255. [8] L. Song and H. Q. Zhang, Appliçation of homotopy analysis method to fraçtional KdV-
Burgers-Kuramoto equation, Physics Letters A 367 (2007), 88-94. [9] H. Jafari and S. Seifi, Homotopy analysis method for solving linear and nonlinear fraçtional
diffusion-wave equation, Communications in Nonlinear Science and Numerical Simulation 14
(2009), 2006-2012.
[10] S. J. Liao, The Proposed Homotopy Analysis Tecnique for the Solution of Nonlinear Problems,
Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai 1992. [11] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman
and Hall/CRC Press, Boça Raton 2003. [12] S. J. Liao, Homotopy analysis method: A new analytiçal teçhnique for nonlinear problems,
Communications in Nonlinear Science and Numerical Simulation 2 (1997), 95-100. [13] S. J. Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics
and Computation 147 (2004), 499-513.
[14] L. Podlubny, Fractional Differantial Equations, Açademiç Press, London 1999.
[15] M. Caputo, Linear models of dissipation whose Q is almost frequençy independent-II, Geo¬physical Journal International 13 (1967), 529-539.
[16] M. Caputo, Elasticita e Dissipazione, Zaniçhelli Publisher, Bologna, 1969.
[17] L. Song, Q. Wang and H. Zhang, Rational approximation solution of the fraçtional Sharma-Tasso-Olever equation, Journal of Computational and Applied Mathematics 224 (2009), 210¬218.
[18] S. J. Liao, Notes on the homotopy analysis method: Some definitions and theorems, Commu¬nications in Nonlinear Science and Numerical Simulation 14 (2009), 983-997.

Thank you for copying data from http://www.arastirmax.com