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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 372741, 6 pages
http://dx.doi.org/10.1155/2014/372741
Research Article

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

1College of Science, Hebei United University, Tangshan 063009, China
2College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
3College of Metallurgy and Energy, Hebei United University, Tangshan 063009, China
4Department of Mathematics, University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, Italy
5School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi 710048, China
6Department of Mechanical Engineering, Bu-Ali Sina University, P.O. Box 65175-4161, Hamedan, Iran
7Qinggong College, Hebei United University, Tangshan 063009, China
8Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China

Received 5 January 2014; Revised 8 February 2014; Accepted 8 February 2014; Published 12 March 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2014 Ai-Min Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A.-M. Wazwaz, “Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations,” Chaos, Solitons & Fractals, vol. 28, no. 4, pp. 1005–1013, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. Yusufoğlu, “The variational iteration method for studying the Klein-Gordon equation,” Applied Mathematics Letters, vol. 21, no. 7, pp. 669–674, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A.-M. Wazwaz, “The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation,” Applied Mathematics and Computation, vol. 167, no. 2, pp. 1179–1195, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. M. El-Sayed, “The decomposition method for studying the Klein-Gordon equation,” Chaos, Solitons & Fractals, vol. 18, no. 5, pp. 1025–1030, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. S. V. Ravi Kanth and K. Aruna, “Differential transform method for solving the linear and nonlinear Klein-Gordon equation,” Computer Physics Communications, vol. 180, no. 5, pp. 708–711, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. S. H. Chowdhury and I. Hashim, “Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations,” Chaos, Solitons & Fractals, vol. 39, no. 4, pp. 1928–1935, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. K. Golmankhaneh, A. K. Golmankhaneh, and D. Baleanu, “On nonlinear fractional KleinGordon equation,” Signal Processing, vol. 91, no. 3, pp. 446–451, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Kurulay, “Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method,” Advances in Difference Equations, vol. 2012, no. 1, article 187, pp. 1–8, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. K. A. Gepreel and M. S. Mohamed, “Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation,” Chinese Physics B, vol. 22, no. 1, Article ID 010201, 2013.
  10. K. M. Kolwankar and A. D. Gangal, “Local fractional Fokker-Planck equation,” Physical Review Letters, vol. 80, no. 2, pp. 214–217, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Carpinteri, B. Chiaia, and P. Cornetti, “Static-kinematic duality and the principle of virtual work in the mechanics of fractal media,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 1-2, pp. 3–19, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. A. K. Golmankhaneh and D. Baleanu, “On a new measure on fractals,” Journal of Inequalities and Applications, vol. 2013, no. 1, article 522, 2013.
  13. A. K. Golmankhaneh, A. K. Golmankhaneh, and D. Baleanu, “Lagrangian and Hamiltonian mechanics on fractals subset of real-line,” International Journal of Theoretical Physics, vol. 52, no. 11, pp. 4210–4217, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. K. G. Alireza, V. Fazlollahi, and D. Baleanu, “Newtonian mechanics on fractals subset of real-line,” Romania Reports in Physics, vol. 65, pp. 84–93, 2013.
  15. A. S. Balankin, “Stresses and strains in a deformable fractal medium and in its fractal continuum model,” Physics Letters A, vol. 377, no. 38, pp. 2535–2541, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, NY, USA, 2012.
  17. A. M. Yang, Y. Z. Zhang, and Y. Long, “The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar,” Thermal Science, vol. 17, no. 3, pp. 707–713, 2013.
  18. S. Q. Wang, Y. J. Yang, and H. K. Jassim, “Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative,” Abstract and Applied Analysis, vol. 2014, Article ID 176395, 7 pages, 2014. View at Publisher · View at Google Scholar
  19. J.-H. He, “Exp-function method for fractional differential equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 14, no. 6, pp. 363–366, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. X.-J. Yang, D. Baleanu, and J.-H. He, “Transport equations in fractal porous media within fractional complex transform method,” Proceedings of the Romanian Academy A, vol. 14, no. 4, pp. 287–292, 2013.
  21. A.-M. Yang, X.-J. Yang, and Z.-B. Li, “Local fractional series expansion method for solving wave and diffusion equations on Cantor sets,” Abstract and Applied Analysis, vol. 2013, Article ID 351057, 5 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. Y. Zhao, D.-F. Cheng, and X.-J. Yang, “Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system,” Advances in Mathematical Physics, vol. 2013, Article ID 291386, 5 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. M. Yang, Z. S. Chen, H. M. Srivastava, and X. -J. Yang, “Application of the local fractional series expansion method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators,” Abstract and Applied Analysis, vol. 2013, Article ID 259125, 6 pages, 2013. View at Publisher · View at Google Scholar