Generalized fractional diffusion equation with arbitrary time varying diffusivity
作者：
Highlights：
• We consider the space-time fractional diffusion equation with a general time-dependent diffusion coefficient (Generalized fractional Batchelors equation).
• We solve the generalized fractional equation analytically using the Laplace-Fourier technique.
• We have interpreted the general solution into three of the most well-known special cases describing anomalous diffusion in physical, biological, and geological systems.
• We illustrate the probability distribution functions and the mean square displacement for each case of the time-dependent diffusion coefficients.
摘要
•We consider the space-time fractional diffusion equation with a general time-dependent diffusion coefficient (Generalized fractional Batchelors equation).•We solve the generalized fractional equation analytically using the Laplace-Fourier technique.•We have interpreted the general solution into three of the most well-known special cases describing anomalous diffusion in physical, biological, and geological systems.•We illustrate the probability distribution functions and the mean square displacement for each case of the time-dependent diffusion coefficients.
论文关键词：Fractional calculus- Anomalous diffusion- Fox’s H-function
论文评审过程：Received 23 March 2021, Revised 3 June 2021, Accepted 9 June 2021, Available online 23 June 2021, Version of Record 23 June 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126449
