On \(q\)-analogues of Caputo derivative and Mittag-Leffler function. (English) Zbl 1157.33325
Summary: 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.
MSC:
| 33D60 | Basic hypergeometric integrals and functions defined by them |
| 33E12 | Mittag-Leffler functions and generalizations |
| 26A33 | Fractional derivatives and integrals |
