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A biomathematical view on the fractional dynamics of cellulose degradation

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Published/Copyright: May 23, 2015
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 18 Issue 3

Abstract

We perform a biomathematical analysis of a model of cellulose degradation with derivative of fractional order γ. In the theory of biopolymers division, the phenomenon of shattering remains partially unexplained by classical models of clusters’ fragmentation. Thus, we first examine the case where the breakup rate H is independent of the size of the cellulose chain breaking up, following by the case where H is proportional to the size of the cellulose chain. Both cases show that the evolution of the biopolymer sizes distribution is governed by a combination of higher transcendental functions, namely the Mittag-Leffler function, the further generalized G-function and the Pochhammer polynomial. In particular, this shows existence of an eigen-property, that is, the system describing fractional cellulose degradation contains replicated and partially replicated fractional poles, whose effects are given by these functions.

Keywords : cellulose degradation; fractional differentiation; replicated fractional poles; higher transcendental functions; generalized functions

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Received: 2014-4-16
Published Online: 2015-5-23
Published in Print: 2015-6-1

© Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Fcaa Related News, Events And Books (Fcaa-Volume 18-3-2015)
  3. Decay solutions for a class of fractional differential variational inequalities
  4. A biomathematical view on the fractional dynamics of cellulose degradation
  5. The spreading property for a prey-predator reaction-diffusion system with fractional diffusion
  6. Fractional variation of Hölderian functions
  7. Periodic disturbance rejection for fractional-order dynamical systems
  8. Successive approximation: A survey on stable manifold of fractional differential systems
  9. When do fractional differential equations have solutions that are bounded by the Mittag--Leffler function ?
  10. On explicit stability conditions for a linear fractional difference system
  11. Fractional differential inclusions in the Almgren sense
  12. Time-optimal control of fractional-order linear systems
  13. Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain
  14. Nonexistence results for a class of evolution equations in the Heisenberg group
  15. High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)
  16. Dyadic nonlocal diffusions in metric measure spaces
  17. Fractional derivative anomalous diffusion equation modeling prime number distribution
  18. Time-fractional diffusion equation in the fractional Sobolev spaces
  19. Continuous time random walk models associated with distributed order diffusion equations
https://doi.org/10.1515/fca-2015-0034
Keywords for this article
cellulose degradation; fractional differentiation; replicated fractional poles; higher transcendental functions; generalized functions

Articles in the same Issue

  1. Frontmatter
  2. Fcaa Related News, Events And Books (Fcaa-Volume 18-3-2015)
  3. Decay solutions for a class of fractional differential variational inequalities
  4. A biomathematical view on the fractional dynamics of cellulose degradation
  5. The spreading property for a prey-predator reaction-diffusion system with fractional diffusion
  6. Fractional variation of Hölderian functions
  7. Periodic disturbance rejection for fractional-order dynamical systems
  8. Successive approximation: A survey on stable manifold of fractional differential systems
  9. When do fractional differential equations have solutions that are bounded by the Mittag--Leffler function ?
  10. On explicit stability conditions for a linear fractional difference system
  11. Fractional differential inclusions in the Almgren sense
  12. Time-optimal control of fractional-order linear systems
  13. Analytical solutions for the multi-term time-space fractional reaction-diffusion equations on an infinite domain
  14. Nonexistence results for a class of evolution equations in the Heisenberg group
  15. High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)
  16. Dyadic nonlocal diffusions in metric measure spaces
  17. Fractional derivative anomalous diffusion equation modeling prime number distribution
  18. Time-fractional diffusion equation in the fractional Sobolev spaces
  19. Continuous time random walk models associated with distributed order diffusion equations
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