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LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN FRACTAL HEAT TRANSFER

ABSTRACT
In this article, we first propose the local fractional Laplace series expansion method, which is a coupling method of series expansion method and Laplace transform via local fractional differential operator. An illustrative example for handling the diffusion equation arising in fractal heat transfer is given.
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PAPER SUBMITTED: 2014-05-30
PAPER REVISED: 2015-01-21
PAPER ACCEPTED: 2015-02-13
PUBLISHED ONLINE: 2015-05-30
DOI REFERENCE: https://doi.org/10.2298/TSCI141010063Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S131 - S135]
REFERENCES
  1. Yang, X. J., Local Fractional Functional Analysis & Its Applications, Asian Academic Publisher Limited, Hong Kong, 2011
  2. Yang, X. -J., Baleanu, D., Srivastava, H. M., Local Fractional Integral Transforms and Applications, Elsevier, 2015
  3. Srivastava, H. M., Raina, R. K., Yang, X.-J., Special Functions in Fractional Calculus and Related Fractional Differintegral Equations, World Scientific, Singapore, 2015
  4. Yang, X. J. Local fractional integral transforms, Progress in Nonlinear Science, 4(2011), 1, pp.1-225
  5. Cattani, C., Srivastava, H. M., Yang, X.-J., Fractional Dynamics, Emerging science publishers, 2015
  6. Zhong, W. P., et al., Applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral, Advanced Materials Research, 461(2012), pp. 306-310
  7. Yang, A. M., et al., The Yang-Fourier transforms to heat-conduction in a semi-infinite fractal bar, Thermal Science, 17(2013), 3, pp.707-713
  8. Yang, X. J., et al., A novel approach to processing fractal signals using the Yang-Fourier transforms, Procedia Engineering, 29(2012), pp.2950-2954
  9. Yang, X. J., et al., Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis, Boundary Value Problems, 2013(2013), 1, pp.1-16
  10. Wang, S. Q., et al., Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative, Abstract and Applied Analysis, 2014(2014), Article ID 176395, pp.1-7
  11. Yang, X. J., Local fractional partial differential equations with fractal boundary problems, Advances in Computational Mathematics and its Applications, 1 (2012), 1, pp.60-63
  12. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53(2014), 11, pp.3698-3718
  13. Zhang, Y. Z., et al., Initial boundary value problem for fractal heat equation in the semi-infinite region by Yang-Laplace transform, Thermal Science, 18(2014), 2, pp.677-681
  14. Zhao, Y., et al., Mappings for special functions on Cantor sets and special integral transforms via local fractional operators, Abstract and Applied Analysis, 2013(2013), Article ID 316978, pp.1-6
  15. Zhao, C. G., et al., The Yang-Laplace transform for solving the IVPs with local fractional derivative, Abstract and Applied Analysis, 2014(2014), Article ID 386459, pp.1-5
  16. Liu, C. F., et al., Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem, Thermal Science, 17(2013), 3, pp.715-721
  17. Yang, A. M., et al., Local fractional Laplace variational iteration method for solving linear partial differential equations with local fractional derivative, Discrete Dynamics in Nature and Society, 2014(2014), Article ID 365981, pp.1-8
  18. Li, Y., et al., Local fractional Laplace variational iteration method for fractal vehicular traffic flow, Advances in Mathematical Physics, 2014(2014), Article ID 649318, pp.1-7
  19. Xu, S., et al., Local fractional Laplace variational iteration method for nonhomogeneous heat equations arising in fractal heat flow, Mathematical Problems in Engineering, 2014(2014), Article ID 914725, pp.1-7
  20. Yang, A. M., et al., Local fractional series expansion method for solving wave and diffusion equations on Cantor sets, Abstract and Applied Analysis, 2013(213), Article ID 351057, pp.1-5
  21. Zhao, Y., et al., Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system, Advances in Mathematical Physics, 2013(2013), Article ID 291386, pp.1-5
  22. Yang, A. M., et al., Application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets, Abstract and Applied Analysis, 2014(2014), Article ID 372741, pp.1-6
  23. Yang, X. J., Advanced local fractional calculus and its applications, World Science, New York, NY, USA, 2012
  24. Yang, X. J., et al., Approximate solutions for diffusion equations on cantor space-time, Proceedings of the Romanian Academy, Series A, 14(2013), 2, pp.127-133
  25. Hao, Y. J., et al., Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates, Advances in Mathematical Physics, 2013(2013), Article ID 754248, pp. 1-5

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