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Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function

  • Yingjie Liang EMAIL logo
Veröffentlicht/Copyright: 13. März 2018
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Fractional Calculus and Applied Analysis
Aus der Zeitschrift Fractional Calculus and Applied Analysis Band 21 Heft 1

Abstract

This study analyzes the complexity of ultraslow diffusion process using both the classical Shannon entropy and its general case with inverse Mittag-Leffler function in conjunction with the structural derivative. To further describe the observation process with information loss in ultraslow diffusion, e.g., some defects in the observation process, two definitions of fractional entropy are proposed by using the inverse Mittag-Leffler function, in which the Pade approximation technique is employed to numerically estimate the diffusion entropy. The results reveal that the inverse Mittag-Leffler tail in the propagator of the ultraslow diffusion equation model adds more information to the original distribution with larger entropy. Smaller value of α in the inverse Mittag-Leffler function indicates more complicated of the underlying ultraslow diffusion and corresponds to higher value of entropy. The proposed definitions of fractional entropy can serve as candidates to capture the information loss in ultraslow diffusion.

MSC 2010: 33E12; 34A08; 94A17; 97K60
Key Words and Phrases: ultraslow diffusion; diffusion entropy; structural derivative; inverse Mittag-Leffler function; fractional entropy

Acknowledgements

The work described in this paper was supported by the Fundamental Research Funds for the Central Universities No. 2017B01114, the National Natural Science Foundation of China No. 11702085.

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Received: 2017-9-30
Published Online: 2018-3-13
Published in Print: 2018-2-23

© 2018 Diogenes Co., Sofia

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
https://doi.org/10.1515/fca-2018-0007
Schlagwörter für diesen Artikel
ultraslow diffusion; diffusion entropy; structural derivative; inverse Mittag-Leffler function; fractional entropy

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–volume 21–1–2018)
  4. Survey Paper
  5. From continuous time random walks to the generalized diffusion equation
  6. Survey Paper
  7. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
  8. Research Paper
  9. Exact and numerical solutions of the fractional Sturm–Liouville problem
  10. Research Paper
  11. Some stability properties related to initial time difference for Caputo fractional differential equations
  12. Research Paper
  13. On an eigenvalue problem involving the fractional (s, p)-Laplacian
  14. Research Paper
  15. Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler function
  16. Research Paper
  17. Time-fractional diffusion with mass absorption under harmonic impact
  18. Research Paper
  19. Optimal control of linear systems with fractional derivatives
  20. Research Paper
  21. Time-space fractional derivative models for CO2 transport in heterogeneous media
  22. Research Paper
  23. Improvements in a method for solving fractional integral equations with some links with fractional differential equations
  24. Research Paper
  25. On some fractional differential inclusions with random parameters
  26. Research Paper
  27. Initial boundary value problems for a fractional differential equation with hyper-Bessel operator
  28. Research Paper
  29. Mittag-Leffler function and fractional differential equations
  30. Research Paper
  31. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point
  32. Research Paper
  33. Differential and integral relations in the class of multi-index Mittag-Leffler functions
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