On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Rajkovic, Predrag, Marinkovic, Sladjana, Stankovic, Miomir (2007)
Fractional Calculus and Applied Analysis
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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.