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

Volume 9, Issue 6, pp 3647--3654 http://dx.doi.org/10.22436/jnsa.009.06.17

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Authors

Rubayyi T. Alqahtani - Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O. Box 65892, Riyadh 11566, Saudi Arabia.

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-Leffler function, since the Mittag-Leffler function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater flowing within an unconfined aquifer.

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Keywords

• Atangana-Baleanu derivatives
• Laplace transforms
• groundwater flow
• unconfined aquifer.

MSC

•  47H10
•  34A08

References

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