Abstract and Applied Analysis

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

Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, and Xiao-Jun Yang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 372741, 6 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607145

Digital Object Identifier
doi:10.1155/2014/372741

Mathematical Reviews number (MathSciNet)
MR3182278

Zentralblatt MATH identifier
07022248

Citation

Yang, Ai-Min; Zhang, Yu-Zhu; Cattani, Carlo; Xie, Gong-Nan; Rashidi, Mohammad Mehdi; Zhou, Yi-Jun; Yang, Xiao-Jun. Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 372741, 6 pages. doi:10.1155/2014/372741. https://projecteuclid.org/euclid.aaa/1412607145


Export citation

References

  • 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.
  • E. Yusufoğlu, “The variational iteration method for studying the Klein-Gordon equation,” Applied Mathematics Letters, vol. 21, no. 7, pp. 669–674, 2008.
  • 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.
  • S. M. El-Sayed, “The decomposition method for studying the Klein-Gordon equation,” Chaos, Solitons & Fractals, vol. 18, no. 5, pp. 1025–1030, 2003.
  • 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.
  • 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.
  • A. K. Golmankhaneh, A. K. Golmankhaneh, and D. Baleanu, “On nonlinear fractional KleinGordon equation,” Signal Processing, vol. 91, no. 3, pp. 446–451, 2011.
  • 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.
  • 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.
  • K. M. Kolwankar and A. D. Gangal, “Local fractional Fokker-Planck equation,” Physical Review Letters, vol. 80, no. 2, pp. 214–217, 1998.
  • 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.
  • A. K. Golmankhaneh and D. Baleanu, “On a new measure on fractals,” Journal of Inequalities and Applications, vol. 2013, no. 1, article 522, 2013.
  • 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.
  • 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.
  • 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.
  • X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, NY, USA, 2012.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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. \endinput