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On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Rajkovic, Predrag;  Marinkovic, Sladjana;  Stankovic, Miomir — 2007

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 33D60, 33E12, 26A33 Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.

The Deformed Trigonometric Functions of two Variables

Marinkovic, Sladjana;  Stankovic, Miomir;  Mulalic, Edin — 2012

Mathematica Balkanica New Series

MSC 2010: 33B10, 33E20 Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed...

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