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Kouri, D., Pandya, N., Williams, C.L., Bodmann, B.G. and Yao, J. (2018) Point Transformations and Relationships among Linear Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem. Applied Mathematics, 9, 178-197.
https://doi.org/10.4236/am.2018.92013

has been cited by the following article:

• TITLE: Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations

  AUTHORS: Jie Yao, Cameron L. Williams, Fazle Hussain, Donald J. Kouri

  KEYWORDS: Generalized Fourier Transform, Anomalous Diffusion, Nonlinear

  JOURNAL NAME: Applied Mathematics, Vol.10 No.12, December 23, 2019

  ABSTRACT: The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion function. The generalized Fourier transform approach is the extension of the Fourier transform method used for the normal diffusion equation. The feasibility of the approach is validated by comparing the numerical result with the exact solution for a point-source. The merit of the numerical method is that it provides a way to calculate anomalous diffusion with an arbitrary initial condition.