https://doi.org/10.1140/epjst/e2013-01965-1
Regular Article
Derivation of a fractional Boussinesq equation for modelling unconfined groundwater
1 Department of Water Engineering, Faculty of Agriculture, University of Kurdistan, Sanandaj, Iran
2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416-95447, Iran
3 Department of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Ankara, Turkey
4 Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, PO Box 80204, Jeddah, 21589, Saudi Arabia
5 Institute of Space Sciences, PO Box MG-23, R 76900, Magurele-Bucharest, Romania
a e-mail: dumitru@cankaya.edu.tr
Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
In this manuscript, a fractional Boussinesq equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq equation was derived. Unlike classical Boussinesq equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq equation are constant and scale-invariant. In addition, the fractional Boussinesq equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.
© EDP Sciences, Springer-Verlag, 2013
