Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative

Abstract and Applied Analysis

Volumn 2014, Issue , 2014, Pages

  Wang, Shun Qin ^a   Yang, Yong Ju ^a   Jassim, Hassan Kamil ^b  

^a NANYANG NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84893184829     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2014/176395     Document Type: Article

References (26)

1. Driver R. D., Ordinary and Delay Differential Equations 1977 20 New York, NY, USA Springer Applied Mathematical Sciences 10.1007/978-1-4684-9467-9 MR0477368
2. Podlubny I., Fractional differential equations 1999 198 San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
3. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science North-Holland Mathematics Studies MR2218073
4. Wazwaz A. M., Partial Differential Equations: Methods and Applications 2002 Rotterdam, The Netherlands Balkema
5. Fan J., He J. H., Fractal derivative model for air permeability in hierarchic porous media. Abstract and Applied Analysis 2012 2012 7 354701 10.1155/2012/354701
6. Heymans N., Podlubny I., Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 2006 45 5 765 771 2-s2.0-33745869026 10.1007/s00397-005-0043-5 (Pubitemid 44027219)
7. Karami H., Babakhani A., Baleanu D., Existence results for a class of fractional differential equations with periodic boundary value conditions and with delay. Abstract and Applied Analysis 2013 2013 8 176180 10.1155/2013/176180
8. Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fractional Calculus Models and Numerical Methods 2012 Hackensack, NJ, USA World Scientific Series on Complexity, Nonlinearity and Chaos 10.1142/9789814355216 MR2894576
9. Hristov J., Heat-balance integral to fractional (half-time) heat diffusion sub-model. Thermal Science 2010 14 2 291 316 2-s2.0-77955895114 10.2298/TSCI1002291H
10. Hristov J., A short-distance integral-balance solution to a strong subdiffusion equation: a weak power-law profile. International Review of Chemical Engineering 2010 2 5 555 563
11. Jafari H., Seifi S., Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. Communications in Nonlinear Science and Numerical Simulation 2009 14 5 2006 2012 2-s2.0-56049100715 10.1016/j.cnsns.2008.05.008 MR2474460 ZBL1221.65278
12. Jafari H., Tajadodi H., He's variational iteration method for solving fractional Riccati differential equation. International Journal of Differential Equations 2010 2010 8 764738 10.1155/2010/764738 MR2607724 ZBL1207.34020
13. Atangana A., Secer A., The time-fractional coupled-Korteweg-de-Vries equations. Abstract and Applied Analysis 2013 2013 8 947986 10.1155/2013/947986 MR3035318 ZBL06209510
14. Atangana A., Kiliçman A., Analytical solutions of boundary values problem of 2D and 3D poisson and biharmonic equations by homotopy decomposition method. Abstract and Applied Analysis 2013 2013 9 380484 10.1155/2013/380484
15. Li C., Wang Y., Numerical algorithm based on Adomian decomposition for fractional differential equations. Computers and Mathematics with Applications 2009 57 10 1672 1681 2-s2.0-65049090377 10.1016/j.camwa.2009.03.079
16. Daftardar-Gejji V., Jafari H., Adomian decomposition: a tool for solving a system of fractional differential equations. Journal of Mathematical Analysis and Applications 2005 301 2 508 518 2-s2.0-10344238128 10.1016/j.jmaa.2004.07. 039 (Pubitemid 39630973)
17. Li C., Qian D., Chen Y., On Riemann-Liouville and Caputo derivatives. Discrete Dynamics in Nature and Society 2011 2011 15 2-s2.0-79959248552 10.1155/2011/562494 562494
18. Yang X. J., Local Fractional Functional Analysis and Its Applications 2011 Hong Kong Asian Academic Publisher
19. Yang X. J., Advanced Local Fractional Calculus and Its Applications 2012 New York, NY, USA World Science
20. Yang X. J., Baleanu D., Fractal heat conduction problem solved by local fractional variation iteration method. Thermal Science 2013 17 2 625 628 10.2298/TSCI121124216Y
21. 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 10.2298/TSCI120826074Y
22. Liu C. F., Kong S. S., Yuan S. J., Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem. Thermal Science 2013 17 3 715 721 10.2298/TSCI120826075L
23. Hao Y.-J., Srivastava H. M., Jafari H., Yang X.-J., Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates. Advances in Mathematical Physics 2013 2013 5 754248 10.1155/2013/754248 MR3079019
24. Yang X.-J., Baleanu D., Tenreiro Machado J. A., Systems of Navier-Stokes equations on Cantor sets. Mathematical Problems in Engineering 2013 2013 8 769724 10.1155/2013/769724 MR3070019
25. Hu M.-S., Agarwal R. P., Yang X.-J., Local fractional Fourier series with application to wave equation in fractal vibrating string. Abstract and Applied Analysis 2012 2012 15 567401 10.1155/2012/567401 MR3004869 ZBL1257.35193
26. Yang X. J., Baleanu D., Zhong W. P., Approximation solutions for diffusion equation on Cantor time-space. Proceeding of the Romanian Academy Series A 2013 14 2 127 133