International Scientific Journal

Authors of this Paper

External Links


In this paper the fractal heat-transfer problem described by the theory of local fractional calculus is considered. The non-differentiable-type solution of the heat-transfer equation is obtained. The characteristic equation method is proposed as a powerful technology to illustrate the analytical solution of the partial differential equation in fractal heat transfer.
PAPER REVISED: 2016-01-15
PAPER ACCEPTED: 2016-01-26
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S751 - S754]
  1. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  2. Jafari, H., et al., A Decomposition Method for Solving Diffusion Equations Via Local Fractional Time Derivative, Thermal Science, 19 (2015), Suppl. 1, pp. S123-S129
  3. 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
  4. Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators, Thermal Science, 19 (2015), 2, pp. 959-966
  5. Xu, S., et al., A Novel Schedule for Solving the Two-Dimensional Diffusion Problem in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S99-S103
  6. 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
  7. 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
  8. 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
  9. Jassim, H. K., et al., Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets Within Local Fractional Operators, Mathematical Problem in Engineering, 2015 (2015), ID 309870
  10. Yang, X. J., et al., Initial-Boundary Value Problems for Local Fractional Laplace Equation Arising in Fractal Electrostatics, Journal of Applied Nonlinear Dynamics, 4 (2015), 3, pp. 349-356
  11. 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
  12. 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
  13. 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
  14. Baleanu, D., et al., Local Fractional Variational Iteration Algorithms for the Parabolic Fokker-Planck Equation Defined on Cantor Sets, Progress in Fractional Differentiation and Applications, 1 (2015), 1, pp. 1-11
  15. Ahmad, J., et al., Analytic Solutions of the Helmholtz and Laplace Equations by Using Local Fractional Derivative Operators, Waves, Wavelets and Fractals: Adv. Anal., 1 (2015), 1, pp. 22-26
  16. Jia, Z., et al., Local Fractional Differential Equations by the Exp-Function Method, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 8, pp. 1845-1849
  17. Zhao, C. G., et al., The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative, Abstract Applied Analysis, 2014 (2014), ID 386459
  18. Zhao, D., et al., Some Fractal Heat-Transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp.1867-1871
  19. Srivastava, H. M., et al., A Novel Computational Technology for Homogeneous Local Fractional PDEs in Mathematical Physics, Applied and Computational Mathematics, 2016, in press

© 2020 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