Application of local fractional series expansion method to solve Klein-Gordon equations on cantor sets

Abstract and Applied Analysis

Volumn 2014, Issue , 2014, Pages

  Yang, Ai Min ^a,b   Zhang, Yu Zhu ^a,b   Cattani, Carlo ^c   Xie, Gong Nan ^d   Rashidi, Mohammad Mehdi ^e   Zhou, Yi Jun ^a   Yang, Xiao Jun ^f  

^a HEBEI UNITED UNIVERSITY   (China)

^b YANSHAN UNIVERSITY   (China)

^c UNIVERSITY OF SALERNO   (Italy)

^d NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^e BU ALI SINA UNIVERSITY   (Iran)

^f CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84897554943     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2014/372741     Document Type: Article

References (23)

1. Wazwaz A.-M., Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos, Solitons & Fractals 2006 28 4 1005 1013 10.1016/j.chaos.2005.08.145 MR2212787 ZBL1099.35125 (Pubitemid 41607601)
2. Yusufoǧlu E., The variational iteration method for studying the Klein-Gordon equation. Applied Mathematics Letters 2008 21 7 669 674 10.1016/j.aml.2007.07.023 MR2423043 ZBL1152.65475 (Pubitemid 351680544)
3. Wazwaz A.-M., The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Applied Mathematics and Computation 2005 167 2 1179 1195 10.1016/j.amc.2004.08.006 MR2169760 ZBL1082.65584 (Pubitemid 41344817)
4. El-Sayed S. M., The decomposition method for studying the Klein-Gordon equation. Chaos, Solitons & Fractals 2003 18 5 1025 1030 10.1016/S0960-0779(02)00647-1 MR1988710 ZBL1068.35069
5. Ravi Kanth A. S. V., Aruna K., Differential transform method for solving the linear and nonlinear Klein-Gordon equation. Computer Physics Communications 2009 180 5 708 711 10.1016/j.cpc.2008.11.012 MR2678291 ZBL1198.81038
6. Chowdhury M. S. H., Hashim I., Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations. Chaos, Solitons & Fractals 2009 39 4 1928 1935 10.1016/j.chaos.2007.06.091 MR2514578 ZBL1197.65164
7. Golmankhaneh A. K., Golmankhaneh A. K., Baleanu D., On nonlinear fractional KleinGordon equation. Signal Processing 2011 91 3 446 451 2-s2.0-78049333706 10.1016/j.sigpro.2010.04.016
8. Kurulay M., Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method. Advances in Difference Equations 2012 2012 1, article 187 1 8 10.1186/1687-1847-2012-187 MR3016697
9. Gepreel K. A., Mohamed M. S., Analytical approximate solution for nonlinear space-time fractional Klein-Gordon equation. Chinese Physics B 2013 22 1 010201
10. Kolwankar K. M., Gangal A. D., Local fractional Fokker-Planck equation. Physical Review Letters 1998 80 2 214 217 10.1103/PhysRevLett.80.214 MR1604435 ZBL0945.82005 (Pubitemid 128621921)
11. Carpinteri A., Chiaia B., Cornetti P., Static-kinematic duality and the principle of virtual work in the mechanics of fractal media. Computer Methods in Applied Mechanics and Engineering 2001 191 1-2 3 19 2-s2.0-0035834542 10.1016/S0045-7825(01)00241-9 (Pubitemid 33105419)
12. Golmankhaneh A. K., Baleanu D., On a new measure on fractals. Journal of Inequalities and Applications 2013 2013 1, article 522
13. Golmankhaneh A. K., Golmankhaneh A. K., Baleanu D., Lagrangian and Hamiltonian mechanics on fractals subset of real-line. International Journal of Theoretical Physics 2013 52 11 4210 4217 10.1007/s10773-013-1733-x MR3108745 ZBL06251914
14. Alireza K. G., Fazlollahi V., Baleanu D., Newtonian mechanics on fractals subset of real-line. Romania Reports in Physics 2013 65 84 93
15. Balankin A. S., Stresses and strains in a deformable fractal medium and in its fractal continuum model. Physics Letters A 2013 377 38 2535 2541 10.1016/j.physleta.2013.07.029 MR3143472
16. Yang X. J., Advanced Local Fractional Calculus and Its Applications 2012 New York, NY, USA World Science Publisher
17. Yang A. M., Zhang Y. Z., Long Y., The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar. Thermal Science 2013 17 3 707 713
18. Wang S. Q., Yang Y. J., Jassim H. K., Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative. Abstract and Applied Analysis 2014 2014 7 176395 10.1155/2014/176395
19. He J.-H., Exp-function method for fractional differential equations. International Journal of Nonlinear Sciences and Numerical Simulation 2013 14 6 363 366 10.1515/ijnsns-2011-0132 MR3118435
20. Yang X.-J., Baleanu D., He J.-H., Transport equations in fractal porous media within fractional complex transform method. Proceedings of the Romanian Academy A 2013 14 4 287 292
21. Yang A.-M., Yang X.-J., Li Z.-B., Local fractional series expansion method for solving wave and diffusion equations on Cantor sets. Abstract and Applied Analysis 2013 2013 5 351057 10.1155/2013/351057 MR3064518
22. Zhao Y., Cheng D.-F., Yang X.-J., Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system. Advances in Mathematical Physics 2013 2013 5 291386 10.1155/2013/291386 MR3102791
23. Yang A. M., Chen Z. S., Srivastava H. M., Yang X. -J., 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 2013 2013 6 259125 10.1155/2013/259125