THERMAL SCIENCE

International Scientific Journal

External Links

THE INTEGRATING FACTOR METHOD FOR SOLVING THE STEADY HEAT TRANSFER PROBLEMS IN FRACTAL MEDIA

ABSTRACT
In this paper, we propose the integrating factor method via local fractional derivative for the first time. We use the proposed method to handle the steady heat-transfer equations in fractal media with the constant coefficients. Finally, we discuss the non-differentiable behaviors of fractal heat-transfer problems.
KEYWORDS
PAPER SUBMITTED: 2015-11-08
PAPER REVISED: 2016-01-11
PAPER ACCEPTED: 2016-01-26
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3729C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S729 - S733]
REFERENCES
  1. Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
  2. Zhang, Y., et al., Local Fractional Variational Iteration Algorithm II for Non-Homogeneous Model Associated with the Non-Differentiable Heat Flow, Advances in Mechanical Engineering, 7 (2015), 10, pp. 1-7
  3. Yan, S. P., Local Fractional Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S131-S135
  4. Zhao, D., et al., On the Fractal Heat-Transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp. 1867-1871
  5. Yang, X. J., Tenreiro Machado, J. A., 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/mma.3765
  6. Yang, X. J., Srivastava, H. M., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communications in Nonlinear Science and Numerical Simulation, 29 (2015), 1, pp. 499-504
  7. Ahmad, J., Mohyud-Din, S. T., Solving Wave and Diffusion Equations on Cantor Sets, Proceeding, Pakistan Academy Science, Islamabad, 2015, Vol. 52, No. 1, pp. 71-77
  8. Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
  9. 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, pp. 752-761
  10. Sun, X., et al., A New Computational Method for the One-Dimensional Diffusion Problem with the Diffusive Parameter Variable in Fractal Media, Thermal Science, 19 (2015), Suppl. 1, pp. S117-S122
  11. Yang, X. J., et al., Local Fractional Variational Iteration Method for Diffusion and Wave Equations on Cantor Sets, Romanian Journal of Physics, 59 (2014), 1-2, pp. 36-48
  12. Srivastava, H. M., et al., Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets, Abstract Applied Analysis, 2014 (2014), ID 620529, pp. 1-7
  13. Zhao, C. G., et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract Applied Analysis, 2014 (2014), ID 386459, pp. 1-5
  14. Zhao, Y., et al., Mappings for Special Functions on Cantor Sets and Special Integral Transforms Via Local Fractional Operators, Abstract Applied Analysis, 2013 (2013), ID 316978, pp. 1-6
  15. Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science, New York, USA, 2012

© 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