TY - JOUR
ID - 3930
TI - New groundwater flow equation with its exact solution
JO - Scientia Iranica
JA - SCI
LA - en
SN - 1026-3098
AU - Atangana, Abdon
AU - Ünlü, Canan
AD - Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State 9300 Bloemfontein, South Africa
AD - Department of Mathematics, Faculty of Sciences, University of Istanbul, 1293 Istanbul, Turkey
Y1 - 2016
PY - 2016
VL - 23
IS - 4
SP - 1837
EP - 1843
KW - New groundwater equation
KW - beta-derivative
KW - analytical methods
KW - simulations
DO - 10.24200/sci.2016.3930
N2 - A new model of groundwater flowing within a confined aquifer was proposed using the concept of local derivative with fractional order. The derivative used in this model obeys all the properties of a local derivative and has a fractional order. The new groundwater flow equation was solved analytically via three different analytical methods. The first method is the well-known method of separation of variable. The problem with this method is the introduction of the Eigen-value that does not have physical meaning. The second method was achieved using novel integral equation called Atangana-transform and this method yields exact solution. An alternative method based on the modified Boltzmann transformation also yields to exact solution. Some numerical simulations were done to express the efficiency of the model
UR - http://scientiairanica.sharif.edu/article_3930.html
L1 - http://scientiairanica.sharif.edu/article_3930_95e717d5a489c4fed9cacb49d36b74fa.pdf
ER -