THERMAL SCIENCE

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Fei Wu

,

Xiao-Jun Yang

APPROXIMATE SOLUTION OF THE NON-LINEAR DIFFUSION EQUATION OF MULTIPLE ORDERS

ABSTRACT
In this paper, fractional diffusion equation of multiple orders is approximately solved. The equation is given in the equivalent integral form. The Adomian polynomial is adopted and analytical solutions are obtained. The result contains two parameters that can have more space for fitting the experiment data.
KEYWORDS
new Adomian polynomials, approximate solution, fractional calculus, non-linear diffusion equation
PAPER SUBMITTED: 2015-12-29
PAPER REVISED: 2016-02-13
PAPER ACCEPTED: 2016-03-15
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3683W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S683 - S687]
REFERENCES
  1. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, Cal., USA, 1999
  2. Metzler, R., et al., The Random Walk's Guide to Anomalous Diffusion: A Fractional Dynamics Approach, Physics Reports, 339 (2000), 1, pp. 11-77
  3. Yang, X. J., et al., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communications in Non-Linear Science and Numerical Simulation, 29 (2015), 1-3, pp. 499-504
  4. Yang, X. J., et al., Fractal Heat Conduction Problem Solved by Local Fractional Variational Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
  5. Das, S., et al., Fractional Diffusion Equations in the Presence of Reaction Terms, Journal of Computational Complexity and Applications, 1 (2015), 1, pp. 15-21
  6. Wu, G. C., et al., Lattice Fractional Diffusion Equation in Terms of A Riesz-Caputo Difference, Phys. A, 438 (2015), NOV., pp. 335-3398
  7. Wu, G. C., et al., Discrete Fractional Logistic Map and Its Chaos, Non-Linear Dynamics, 75 (2014), 1, pp. 283-287
  8. Guo, B. B., et al., Numerical Application for Volterra's Population Growth Model with Fractional Order by the Modified Reproducing Kernel Method, J. Computational Complexity and Applications, 1 (2015), 1, pp. 1-9
  9. Zhao, D. F., et al., A Note on Riemann Diamond Integrals on Time Scales, Journal of Computational Complexity and Applications, 2 (2016), 2, pp. 64-72
  10. Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Springer, N. Y., USA, 1994
  11. Daftardar-Gejji, V., et al., Adomian Decomposition: A Tool for Solving A System of Fractional Differential Equations, Journal of Mathematical Analysis and Applications, 301 (2005), 2, pp. 508-518
  12. Saha, R. S., et al., An Approximate Solution of a Non-Linear Fractional Differential Equation by Adomian Decomposition Method, Applied Mathematics and Computation, 167 (2005), 1, pp. 561-571
  13. Duan, J. S., Recurrence Triangle for Adomian Polynomials, Applied Mathematics and Computation, 216 (2010), 4, pp. 1235-1241
  14. Duan, J. S., et al., Higher-Order Numeric Wazwaz-El-Sayed Modified Adomian Decomposition Algorithms, Computers & Mathematics with Applications, 63 (2012), 11, pp. 1557-1568
  15. Duan, J. S., et al., Solutions of the Initial Value Problem for Non-Linear Fractional Ordinary Differential Equations by the Rach-Adomian-Meyers Modified Decomposition Method, Applied Mathematics and Computation, 218 (2012), 17, pp. 8370-8392
  16. Yang, X. J., et al., Approximate Solutions for Diffusion Equations on Cantor Space-Time, Proceedings, Romanian Academy, Series A, 14 (2013), 2, pp. 127-133
  17. Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators, Thermal Science, 3 (2015), 19, pp. 959-966
  18. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
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Approximate solution of the non-linear diffusion equation of multiple orders

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