Atangana-baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

Abstract

The power law has been used to construct the derivative with fractional order in Caputo and Riemann- Liouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffer function, since the Mittag-Leffer function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater owing within an unconfined aquifer.