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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 632309, 6 pages
Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method
1School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
2Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
4Institute of Space Sciences, Magurele, 077125 Bucharest, Romania
5Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China
Received 12 May 2013; Accepted 13 June 2013
Academic Editor: H. Srivastava
Copyright © 2013 Yong-Ju 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, London, UK, 2010.
- J. Klafter, S. C. Lim, and R. Metzler, Fractional Dynamics in Physics: Recent Advances, World Scientific, Singapore, 2012.
- G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2008.
- D. Baleanu, J. A. Tenreiro Machado, and A. C. J. Luo, Fractional Dynamics and Control, Springer, New York, NY, USA, 2012.
- J. A. Tenreiro Machado, A. C. J. Luo, and D. Baleanu, Nonlinear Dynamics of Complex Systems: Applications in Physical, Biological and Financial Systems, Springer, New York, NY, USA, 2011.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- S. A. El-Wakil, M. A. Madkour, and M. A. Abdou, “Application of Exp-function method for nonlinear evolution equations with variable coefficients,” Physics Letters A, vol. 369, no. 1-2, pp. 62–69, 2007.
- S. Das, “Analytical solution of a fractional diffusion equation by variational iteration method,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 483–487, 2009.
- S. Momani and Z. Odibat, “Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 910–919, 2007.
- S. T. Mohyud-Din, M. A. Noor, and K. I. Noor, “Some relatively new techniques for nonlinear problems,” Mathematical Problems in Engineering, vol. 2009, Article ID 234849, 25 pages, 2009.
- H. Jafari and S. Seifi, “Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2006–2012, 2009.
- J. Hristov, “Heat-balance integral to fractional (half-time) heat diffusion sub-model,” Thermal Science, vol. 14, no. 2, pp. 291–316, 2010.
- G.-c. Wu and E. W. M. Lee, “Fractional variational iteration method and its application,” Physics Letters A, vol. 374, no. 25, pp. 2506–2509, 2010.
- Y. Khan, N. Faraz, A. Yildirim, and Q. Wu, “Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2273–2278, 2011.
- Z. Zhao and C. Li, “Fractional difference/finite element approximations for the time-space fractional telegraph equation,” Applied Mathematics and Computation, vol. 219, no. 6, pp. 2975–2988, 2012.
- W. Deng, “Finite element method for the space and time fractional Fokker-Planck equation,” SIAM Journal on Numerical Analysis, vol. 47, no. 1, pp. 204–226, 2008.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, Hackensack, NJ, USA, 2012.
- X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic, Hong Kong, China, 2011.
- X. J. Yang, “Local fractional integral transforms,” Progress in Nonlinear Science, vol. 4, pp. 1–225, 2011.
- X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
- 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 and A. Sapora, “Diffusion problems in fractal media defined on Cantor sets,” ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 90, no. 3, pp. 203–210, 2010.
- G. Jumarie, “Probability calculus of fractional order and fractional Taylor's series application to Fokker-Planck equation and information of non-random functions,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1428–1448, 2009.
- Y. Khan, Q. Wu, N. Faraz, A. Yildirim, and M. Madani, “A new fractional analytical approach via a modified Riemann-Liouville derivative,” Applied Mathematics Letters, vol. 25, no. 10, pp. 1340–1346, 2012.
- Y. Khan, N. Faraz, S. Kumar, and A. Yildirim, “A coupling method of homotopy perturbation and Laplace transformation for fractional models,” “Politehnica” University of Bucharest, vol. 74, no. 1, pp. 57–68, 2012.
- M. S. Hu, D. Baleanu, and X. J. Yang, “One-phase problems for discontinuous heat transfer in fractal media,” Mathematical Problems in Engineering, vol. 2013, Article ID 358473, 3 pages, 2013.
- W.-H. Su, X.-J. Yang, H. Jafari, and D. Baleanu, “Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator,” Advances in Difference Equations, vol. 2013, article 97, 2013.
- X. J. Yang and D. Baleanu, “Fractal heat conduction problem solved by local fractional variation iteration method,” Thermal Science, vol. 17, no. 2, pp. 625–628, 2013.
- W.-H. Su, D. Baleanu, X.-J. Yang, and H. Jafari, “Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method,” Fixed Point Theory and Applications, vol. 2013, article 89, 2013.
- Y. J. Yang, D. Baleanu, and X. J. Yang, “A local fractional variational iteration method for Laplace equation within local fractional operators,” Abstract and Applied Analysis, vol. 2013, Article ID 202650, 6 pages, 2013.
- M.-S. Hu, R. P. Agarwal, and X.-J. Yang, “Local fractional Fourier series with application to wave equation in fractal vibrating string,” Abstract and Applied Analysis, vol. 2012, Article ID 567401, 15 pages, 2012.
- Y. Zhang, A. Yang, and X. J. Yang, “1-D heat conduction in a fractal medium: a solution by the local fractional Fourier series method,” Thermal Science, 2013.
- G. A. Anastassiou and O. Duman, In Applied Mathematics and Approximation Theory, Springer, New York, NY, USA, 2013.