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Continuous time random walk models associated with distributed order diffusion equations

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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

In this paper continuous time and discrete random walk models approximating diffusion processes associated with time-fractional and spacedistributed order differential equations are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is the inverse to a Levy’s stable subordinator with the stability index β ∈ (0, 1). In the paper the convergence of modeled continuous time and discrete random walks to time-changed processes associated with distributed order fractional diffusion equations are proved using an analytic method.

Keywords : random walk; continuous time random walk; fractional order derivative; stochastic process; time-changed process; fractional order differential equation; pseudo-differential operator; Lèvy process; stable subordinator

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Received: 2014-12-14
Published Online: 2015-5-23
Published in Print: 2015-6-1

© Diogenes Co., Sofia

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  8. Successive approximation: A survey on stable manifold of fractional differential systems
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https://doi.org/10.1515/fca-2015-0049
Keywords for this article
random walk; continuous time random walk; fractional order derivative; stochastic process; time-changed process; fractional order differential equation; pseudo-differential operator; Lèvy process; stable subordinator

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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