New direction in fractional differentiation

Volume 1, Issue 1, pp 18--25

Publication Date: 2017-10-22


A. Atangana - Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa.
I. 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.


Atangana-Baleanu fractional derivatives, Weyl approach, Prabhakar Mittag-Leffler function, integral transform


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