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Updated: Jun 24, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Fundamental solution of the time-space bi-fractional diffusion equation with a kinetic source term for anomalous
Anis Allagui1,2, Georgii Paradezhenko3, Anastasiia Pervishko3
1Department of Sustainable and Renewable Energy Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates. aallagui@sharjah.ac.ae.
Abstract:
The purpose of this paper is to study the fundamental solution of the time-space bi-fractional diffusion equation incorporating an additional kinetic source term in semi-infinite space. The equation is a generalization of the integer-order model (also known as the Debye-Falkenhagen equation) by replacing the first-order time derivative with the Caputo fractional derivative of order , and the second-order space derivative with the Riesz-Feller fractional derivative of order . Using the Laplace-Fourier transforms method, it is shown that the parametric solutions are expressed in terms of the Fox's H-function that we evaluate for different values of and .
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