| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|
|
|---|---|---|
| Article Number | 306 | |
| Number of page(s) | 13 | |
| DOI | https://doi.org/10.1051/mmnp/2018075 | |
| Published online | 15 February 2019 | |
Fractional advection–diffusion equation with memory and Robin-type boundary condition
1
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: dumitru.vieru@tuiasi.ro
Received:
6
May
2018
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.