Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|Number of page(s)||13|
|Published online||15 February 2019|
Fractional advection–diffusion equation with memory and Robin-type boundary condition
Khwaja Fareed University of Engineering & Information Technology,
Rahim Yar Khan, Pakistan.
2 Technical University “Gheorghe Asachi” of Iasi, Iasi, Romania.
3 Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
* Corresponding author: firstname.lastname@example.org
Accepted: 10 November 2018
The one-dimensional fractional advection–diffusion equation with Robin-type boundary conditions is studied by using the Laplace and finite sine-cosine Fourier transforms. The mathematical model with memory is developed by employing the generalized Fick’s law with time-fractional Caputo derivative. The influence of the fractional parameter (the non-local effects) on the solute concentration is studied. It is found that solute concentration can be minimized by decreasing the memory parameter. Also, it is found that, at small values of time the ordinary model leads to minimum concentration, while at large values of the time the fractional model is recommended.
Mathematics Subject Classification: 35Q35
Key words: Advection / diffusion / Caputo derivative / analytical solution
© EDP Sciences, 2019
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