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Caputo \(q\)-fractional initial value problems and a \(q\)-analogue Mittag-Leffler function. (English) Zbl 1231.26006

Summary: Caputo \(q\)-fractional derivatives are introduced and studied. A Caputo -type \(q\)-fractional initial value problem is solved and its solution is expressed by means of a new introduced \(q\)-Mittag – Leffler function. Some open problems about \(q\)-fractional integrals are proposed as well.

MSC:

26A33 Fractional derivatives and integrals
26E70 Real analysis on time scales or measure chains
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