New direction in fractional differentiation

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Authors
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.
Abstract
Based upon the MittagLeffler 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 MittagLeffler function known as Prabhakar function. Some new results are presented together with some
applications.
Keywords
 AtanganaBaleanu fractional derivatives
 Weyl approach
 Prabhakar MittagLeffler function
 integral transform
References
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