Geodesic
On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 359-373.

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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.
Keywords: Mittag-Leffler Function, q–Integral, q–Derivative, Fractional Integral, Fractional Derivative, 33D60, 33E12, 26A33 
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Rajkovic, Predrag; Marinkovic, Sladjana; Stankovic, Miomir. On q–Analogues of Caputo Derivative and Mittag–Leffler Function. Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 359-373. http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a1/