New direction in fractional differentiation


Abdon Atangana - Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa. Ilknur Koca - Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey.


Based upon the Mittag-Leffler function, new derivatives with fractional order were constructed. With the same line of idea, improper derivatives based on the Weyl approach are constructed in this work. To further model some complex physical problems that cannot be modeled with existing derivatives with fractional order, we propose, a new derivative based on the more generalized Mittag-Leffler function known as Prabhakar function. Some new results are presented together with some applications.

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ISRP Style

Abdon Atangana, Ilknur Koca, New direction in fractional differentiation, Mathematics in Natural Science, 1 (2017), no. 1, 18--25

AMA Style

Atangana Abdon, Koca Ilknur, New direction in fractional differentiation. Math. Nat. Sci. (2017); 1(1):18--25

Chicago/Turabian Style

Atangana, Abdon, Koca, Ilknur. "New direction in fractional differentiation." Mathematics in Natural Science, 1, no. 1 (2017): 18--25



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