Mittag-Leffler Function q–Integral q–Derivative Fractional Integral Fractional Derivative 33D60 33E12 26A33
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 10, No 4, (2007), 359p-373p
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.