THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jie-Dong Chen

,

Hua-Ping Li

THE NON-DIFFERENTIABLE SOLUTION FOR LOCAL FRACTIONAL LAPLACE EQUATION IN STEADY HEAT-CONDUCTION PROBLEM

ABSTRACT
In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM) via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.
KEYWORDS
heat-conduction problem, Laplace equation, analytical solution, local fractional derivative
PAPER SUBMITTED: 2015-12-21
PAPER REVISED: 2016-01-05
PAPER ACCEPTED: 2016-01-28
PUBLISHED ONLINE: 2016-08-14
DOI REFERENCE: https://doi.org/10.2298/TSCI151221200C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S769 - S772]
REFERENCES
  1. D., Zhao., et al., Some Fractal Heat-transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp.1867-1871
  2. Yang, X. J., et al., Cantor-type Cylindrical-coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letter A, 377(2013), 28, pp.1696-1700
  3. X.-J. Yang, et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67 (2015), pp.752-761.
  4. Yang, X. J., et al., Local Fractional Similarity Solution for The Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47(2015), pp.54-60
  5. 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), pp.143-151
  6. A.M. Yang, et al., Local Fractional Fourier Series Solutions for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow with Local Fractional Derivative, Advances in Mechanical Engineering, 2014 (2014), pp.1-5
  7. Yang, X. J., Baleanu, D., Srivastava, H. M., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, 2015
  8. Y. Y. Li, et al., Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain, Advances in Mathematical Physics, 2014 (2014), pp.1-5
  9. X.-J. Yang, et al., Initial-boundary Value Problems for Local Fractional Laplace Equation Arising in Fractal Electrostatics, Journal of Applied Nonlinear Dynamics, 4 (2015), pp.349-356
  10. Ahmad, J., et al., Analytic Solutions of The Helmholtz and Laplace Equations by Using Local Fractional Derivative Operators, Waves, Wavelets and Fractals, 1 (2015) 22-26
  11. Cattani, C., Srivastava, H. M., Yang, X. J., Fractional Dynamics, Emerging Science Publishers, 2015
  12. 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), pp.1-5
  13. Yang, Y. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation Within
  14. Srivastava, H. M., et al., A Novel Computational Technology for Homogeneous Local Fractional PDEs in Mathematical Physics, 2015, finished
PDF VERSION [DOWNLOAD]
The non-differentiable solution for local fractional Laplace equation in steady heat-conduction problem

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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