THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Yan-Mei Qin

,

Hua Kong

,

Kai-Teng Wu

,

Xiao-Ming Zhu

DISCRETE FRACTIONAL DIFFUSION MODEL WITH TWO MEMORY TERMS

ABSTRACT
Fractional calculus can always exactly describe anomalous diffusion. Recently the discrete fractional difference is becoming popular due to the depiction of non-linear evolution on discrete time domains. This paper proposes a diffusion model with two terms of discrete fractional order. The numerical simulation is given to reveal various diffusion behaviors.
KEYWORDS
discrete fractional diffusion equation of two terms, discrete fractional difference
PAPER SUBMITTED: 2014-12-08
PAPER REVISED: 2015-07-20
PAPER ACCEPTED: 2015-07-28
PUBLISHED ONLINE: 2015-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI1504177Q
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 4, PAGES [1177 - 1181]
REFERENCES
  1. Fan, Z., et al., Experimental Investigation of Dispersion during Flow of Multi-Walled Carbon Nanotube/ Polymer Suspension in Fibrous Porous Media, Carbon, 42 (2004), 4, pp. 871-876
  2. Lysenko, V., et al., Gas Permeability of Porous Silicon Nanostructures, Physical Review, E, 70 (2004), 1, 017301
  3. Uchida, T., et al., Effects of Pore Sizes on Dissociation Temperatures and Pressures of Methane, Carbon Dioxide, and Propane Hydrates in Porous Media, The Journal of Physical Chemistry. B, 106 (2002), 4, pp. 820-826
  4. Carpinteri, A., Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials, International Journal of Solids and Structures, 31 (1994), 3, pp. 291-302
  5. Zhao, L., et al., Fractal Approach to Flow through Porous Material, International Journal of Non-Linear Sciences and Numerical Simulation, 10 (2009), 7, pp. 897-902
  6. He, J.-H., A New Fractal Derivation, Thermal Science, 15 (2011), Suppl. 1, pp. S145-S147
  7. Wang, Q. L., et al., Fractional Model for Heat Conduction in Polar Bear Hairs, Thermal Science, 16 (2012), 2, pp. 339-342
  8. Carpinteri, A., Mainardi, F., Fractals and Fractional Calculus in Continuum Mechanics, vol. 378, Springer, Wien, 2014
  9. Protic, M. Z., et al., Application of Fractional Calculus in Ground Heat Flux Estimation, Thermal Science, 16 (2012), 2, pp. 373-384
  10. Yang, F., et al., The Inverse Source Problem for Time-Fractional Diffusion Equation: Stability Analysis and Regularization, Inverse Problems in Science and Engineering, 23 (2015), 6, pp. 969-996
  11. Angstmann, C. N., et al., A Discrete Time Random Walk Model for Anomalous Diffusion, Journal of Computational Physics, 293 (2015), Aug., pp. 53-69
  12. He, J.-H., Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media, Comput. Method Applied Mechanics and Engineering, 167 (1998), 1-2, pp. 57-68
  13. Diethelm, K., et al., A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations, Non-Linear Dynamics, 29 (2002), 1-4, pp. 3-22
  14. Liu, F., et al., Numerical Solution of the Space Fractional Fokker-Planck Equation, Journal of Computational and Applied Mathematics, 166 (2004), 1, pp. 209-219
  15. Liu, F., et al., Stability and Convergence of the Difference Methods for the Space-Time Fractional Advection- Diffusion Equation, Applied Mathematics and Computation, 191 (2007), 1, pp. 12-20
  16. Hristov, J., Heat-Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2010), 2, pp. 291-316
  17. Duan, J. S., Rach, R., A New Modification of the Adomian Decomposition Method for Solving Boundary Value Problems for Higher Order Non-Linear Differential Equations, Applied Mathematics and Computation, 218 (2011), 8, pp. 4090-4118
  18. Hristov, J., Approximate Solutions to Fractional Subdiffusion Equations, The European Physical Journal Special Topics, 193 (2011), 1, pp. 229-243
  19. Baleanu, D., et al., Fractional Calculus Models and Numerical Methods, Complexity, Non-Linearity and Chaos, World Scientific, Boston, Mass., USA , 2012
  20. Duan, J. S., et al., A Review of the Adomian Decomposition Method and Its Applications to Fractional Differential Equations, Communications in Fractional Calculus, 3 (2012), 2, pp. 73-99
  21. Atici, F. M., Eloe, P. W., A Transform Method in Discrete Fractional Calculus, International Journal of Difference Equations, 2 (2007), 2, pp. 165-176
  22. Atici, F. M., Eloe, P. W., Initial Value Problems in Discrete Fractional Calculus, Proceedings of the American Mathematical Society, 137 (2009), 3, pp. 981-989
  23. Abdeljawad, T., On Riemann and Caputo Fractional Differences, Computers & Mathematics with Applications, 62 (2011), 3, pp. 1602-1611
  24. Anastassiou, G. A., About Discrete Fractional Calculus with Inequalities, in: Intelligent Mathematics (Eds. J. Kacprzyk, L. Jain), Computational Analysis, Springer, Berlin, 2011, pp. 575-585
  25. Wu, G. C., Baleanu, D., Discrete Fractional Logistic Map and Its Chaos, Non-Linear Dynamics, 75 (2014), 1-2, pp. 283-287
  26. Wu, G. C., Baleanu, D., Chaos Synchronization of the Discrete Fractional Logistic Map, Signal Processing, 102 (2014), Sept., pp. 96-99
  27. Wu, G. C., Baleanu, D., Jacobian Matrix Algorithm for Lyapunov Exponents of the Discrete Fractional Maps, Communications in Non-Linear Science and Numerical Simulation, 22 (2015), 1-3, pp. 95-100
  28. Wu, G. C., et al., Discrete Fractional Diffusion Equation, Non-Linear Dynamics, 80 (2015), 1-2, pp. 1-6
PDF VERSION [DOWNLOAD]
DISCRETE FRACTIONAL DIFFUSION MODEL WITH TWO MEMORY TERMS

© 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