DISTRIBUTED ORDER FRACTIONAL SUB-DIFFUSION

By M. Naber. 2003

163 citations recorded by the source corpus.

A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper, sub-diffusive cases are considered. That is, the order of the time derivative ranges from zero to one. The equation is solved for Dirichlet, Neumann and Cauchy boundary conditions. The time dependence for each of the three cases is found to be a functional of the diffusion parameter. This functional is shown to have decay properties. Upper and lower bounds are computed for the functional. Examples are also worked out for comparative decay rates.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5dc0d07cb0c30009d075b483a302103cb1b879cf

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In Applied Mathematics

1. Anatoly N. Kochubei
2. Palaniappan Vellaisamy
3. Mark M. Meerschaert
4. Erkan Nane
5. Stevan Pilipovic
6. Teodor M. Atanackovic
7. Dušan Zorica
8. Yuri Luchko

In Modeling and Simulation

1. Anatoly N. Kochubei
2. Palaniappan Vellaisamy
3. Erkan Nane
4. Mark M. Meerschaert
5. Teodor M. Atanackovic
6. Stevan Pilipovic
7. Dušan Zorica
8. Vasily E. Tarasov

In Numerical Analysis

1. Mark M. Meerschaert
2. Teodor M. Atanackovic
3. Stevan Pilipovic
4. Dušan Zorica
5. Erkan Nane
6. Palaniappan Vellaisamy
7. Anatoly N. Kochubei
8. Vasily E. Tarasov

Citations in the corpus

• Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations (2014, unknown): “, [3]-[4], [15], [17], [21] and the references therein).”
• Distributed order calculus and equations of ultraslow diffusion (2007, background): “A number of recent publications by physicists (see [3, 4, 5, 25 , 38] and references there) is devoted to the case where the mean square displacement has a logarithmic growth.”
• Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations (2009, methodology): “Time distributed-order diffusion equations were solved by Naber (2004) for the Dirichlet, Neumann and Cauchy problems.”
• Distributed-order fractional diffusions on bounded domains (2009, background): “A mixture of power laws leads to a distributed-order fractional derivative in time [8,26,29].”
• Time-fractional Diffusion of Distributed Order (2007, unknown): “in [7, 9, 10, 11, 46 , 51] whereas the R-L form e.g.”