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Similarity Solution for Fractional Diffusion Equation [PDF]
Abstract and Applied Analysis, 2014 Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent.
Jun-Sheng Duan, Ai-Ping Guo, Wen-Zai Yun
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Fractional Advection-Diffusion-Asymmetry Equation [PDF]
Physical Review Letters, 2020 Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems. Motivated by work on contaminant spreading in geological formations we propose and investigate a fractional ...
Wanli Wang, Eli Barkai
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Fractional chemotaxis diffusion equations [PDF]
Physical Review E, 2010 We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding.
Langlands, T. A. M., Henry, B. I.
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Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics, 2021 By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional ...
Chao Yue +3 more
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Supplement a high-dimensional time fractional diffusion equation
Alexandria Engineering Journal, 2023 In this article, we discussed a high-dimensional time fractional diffusion equation which is used to write many nonlinear phenomena in three dimensional space diffusion processes.
Jian-Gen Liu, Fa-Zhan Geng, Xin Li
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Fractional Diffusion Equations [PDF]
, 2018 The Riemann-Liouville fractional integrals and derivatives. There exist many definitions of fractional derivatives and integrals, which are meaningful for different classes of functions, inspired by various applications etc. See [202] for a general survey and a detailed exposition of many aspects of the fractional calculus.
Samuil D. Eidelman +2 more
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Fractional reaction-diffusion equation [PDF]
The Journal of Chemical Physics, 2003 A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect.
Seki, Kazuhiko +2 more
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Semi-Fractional Diffusion Equations [PDF]
Fractional Calculus and Applied Analysis, 2019 32 pages, 5 ...
Kern, Peter +2 more
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Fractional-calculus diffusion equation [PDF]
Nonlinear Biomedical Physics, 2010 Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems.The canonical quantization of a system represented classically by one-dimensional Fick's law, and the ...
Ajlouni, Abdul-Wali M. S. +1 more
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Fractional Reaction-Diffusion Equations [PDF]
Astrophysics and Space Science, 2006 LaTeX, 17 pages, corrected ...
Saxena, R. K. +2 more
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