THERMAL SCIENCE

International Scientific Journal

ADOMIAN DECOMPOSITION METHOD FOR THREE-DIMENSIONAL DIFFUSION MODEL IN FRACTAL HEAT TRANSFER INVOLVING LOCAL FRACTIONAL DERIVATIVES

ABSTRACT
The non-differentiable analytical solution of the 3-D diffusion equation in fractal heat transfer is investigated in this article. The Adomian decomposition method is considered in the local fractional operator sense. The obtained result is given to show the sample and efficient features of the presented technique to implement fractal heat transfer problems.
KEYWORDS
PAPER SUBMITTED: 2014-11-11
PAPER REVISED: 2015-02-02
PAPER ACCEPTED: 2015-02-28
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S37F
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S137 - S141]
REFERENCES
  1. Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong, 2011
  2. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  3. Yang, X. J., et al., Cantor-Type Cylindrical-Coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letters A, 377 (2013), 28-30, pp. 1696-1700
  4. 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
  5. Christianto, V., Rahul, B., A Derivation of Proca Equations on Cantor Sets: a Local Fractional Approach, Bulletin of Mathematical Sciences & Applications, 3 (2014), 4, pp. 75-87
  6. 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.
  7. Yang, X.-J., et al. , Modeling Fractal Waves on Shallow Water Surfaces via Local Fractional Kortewegde Vries Equation, Abstract and Applied Analysis, 2014 (2014), ID 278672
  8. Zhang, Y., et al., On a Local Fractional Wave Equation under Fixed Entropy Arising in Fractal Hydrodynamics, Entropy, 16 (2014), 12, pp. 6254-6262
  9. 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), ID 754248
  10. Yang, X. J., et al., Approximation Solutions for Diffusion Equation on Cantor Time-Space, Proceeding of the Romanian Academy A, 14 (2013), 2, pp. 127-133
  11. Yan, S. P., et al., Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 (2014), ID 161580
  12. 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

© 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