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EXACT SOLUTIONS FOR THE DIFFERENTIAL EQUATIONS IN FRACTAL HEAT TRANSFER

ABSTRACT
In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.
KEYWORDS
PAPER SUBMITTED: 2015-12-12
PAPER REVISED: 2016-01-21
PAPER ACCEPTED: 2016-01-25
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3747Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S747 - S750]
REFERENCES
  1. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  2. Cattani, C., Local Fractional Calculus on Shannon Wavelet Basis, Chapter 1, in: Fractional Dynamics (Eds. C. Cattani et al.), Walter de Gruyter GmbH & Co KG, Berlin 2016
  3. Yang, X. J., et al., A New Insight into Complexity from the Local Fractional Calculus View point: Modelling Growths of Populations, Mathematical Methods in the Applied Sciences, 2015, DOI.10.1002/wwa3765
  4. Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84 (2016), 1, pp. 3-7
  5. Baleanu, D., et al., Local Fractional Variational Iteration Algorithms for the Parabolic Fokker-Planck Equation Defined on Cantor Sets, Prog. Fract. Differ. Appl., 1 (2015), 1, pp. 1-11
  6. Ahmad, J., et al., Analytic Solutions of the Helmholtz and Laplace Equations by Using Local Fractional Derivative Operators, Waves, Wavelets and Fractals, 1 (2015), 1, pp. 22-26
  7. Ahmad, J. S., Mohyud-Din, T., Solving Wave and Diffusion Equations on Cantor Sets, Proceeding, Pakistan Academy Science, 2015, Vol. 52, No 1, pp. 71-77
  8. Zhao, D., et al., Some Fractal Heat-Transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp. 1867-1871.
  9. Wang, Y., et al., Solving Fractal Steady Heat-Transfer Problems with the Local Fractional Sumudu Transform, Thermal Science, 19 (2015), Suppl. 2, pp. S637-S641
  10. ***, Fractional Dynamics (Eds. C. Cattani, H. M. Srivastava, X.-J. Yang), De Gruyter Open, Berlin, 2015, ISBN 978-3-11-029316-6
  11. Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151

© 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