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A NEW COMPUTATIONAL METHOD FOR THE ONE-DIMENSIONAL DIFFUSION PROBLEM WITH THE DIFFUSIVE PARAMETER VARIABLE IN FRACTAL MEDIA

ABSTRACT
In this paper, we use a local fractional Laplace decomposition method to solve the diffusion equation with the diffusive parameter variable in fractal media. The obtained result illustrates the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
KEYWORDS
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-01-22
PAPER ACCEPTED: 2015-02-12
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S17S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S117 - S122]
REFERENCES
  1. Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science, New York, USA, 2012
  2. Yang, X. J., Local Fractional Integral Transforms, Progress in Nonlinear Science, 4(2011), 1, pp. 1-225
  3. Yang, X. J., Local Fractional Functional Analysis & Its Applications, Asian Academic Publisher, Hong Kong, 2011
  4. Zhao, Y., et al., Maxwell’s Equations on Cantor Sets: a Local Fractional Approach, Advances in High Energy Physics, 2013 (2013), ID 686371
  5. Kolwankar, K. M., Gangal, A. D., Local Fractional Fokker-Planck Equation, Physical Review Letters, 80(1998), 2, pp. 2-14
  6. Yang, X. J., et al., Mathematical Aspects of the Heisenberg Uncertainty Principle within Local Fractional Fourier Analysis, Boundary Value Problems, 2013(2013), 1, May, pp. 1-16
  7. Yang, X. J., et al., Cantor-Type Cylindrical-Coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letters A, 377(2013), 28, pp. 1696-1700
  8. Carpinteri, A., Cornetti, P., A Fractional Calculus Approach to the Description of Stress and Strain Localization in Fractal Media, Chaos, Solitons & Fractals, 13 (2002), 1, pp. 85-94
  9. Zhang, Y., et al., On a Local Fractional Wave Equation under Fixed Entropy Arising in Fractal Hydrodynamics, Entropy, 16(2014), 12, pp. 6254-6262
  10. Carpinteri, A., et al., Static-Kinematic Duality and the Principle of Virtual Work in the Mechanics of Fractal Media, Computer Methods in Applied Mechanics and Engineering, 191(2001), 1, pp. 3-19
  11. Yang, X. J., et al., Systems of Navier-Stokes Equations on Cantor Sets, Mathematical Problems in Engineering, 2013 (2013), ID 769724
  12. Carpinteri, A., et al. , On the Mechanics of Quasi-Brittle Materials with a Fractal Microstructure, Engineering Fracture Mechanics, 70(2003), 16, pp. 2321-2349
  13. Yang, X. J., et al., On Local Fractional Continuous Wavelet Transform, Abstract and Applied Analysis, 2013(2013), ID 725416
  14. Zhao, Y. et al., Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets, Mathematical Problems in Engineering, 2013(2013), ID 560932
  15. Chen, Z. Y., et al., Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach, Advances in Mathematical Physics, 2014(2014), ID 561434
  16. Yan, S. P., et al., Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014(2014), ID 161580
  17. Cao, Y., et al., Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets, Abstract and Applied Analysis 2014(2014), ID 803693
  18. 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), ID 176395
  19. Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67 (2015), 3, in press
  20. Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250
  21. Yang, A. M., et al., The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method, Advances in Mathematical Physics, 2014(2014), ID 983254
  22. Baleanu, D., et al., Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators, Abstract and Applied Analysis, 2014 (2014), ID 535048
  23. 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), 2, pp.306-310
  24. 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
  25. 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
  26. Zhao, C. G., et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract and Applied Analysis 2014 (2014), ID 386459
  27. 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
  28. Cattani, C., et al., Fractional Dynamics, Emerging science publishers, 2015
  29. Srivastava, H. M., et al., Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract and Applied Analysis, 2014 (2014), ID 620529

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence