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On Riemann and Caputo fractional differences. (English) Zbl 1228.26008
Summary: We define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before. Also, the discrete version of the $Q$-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions.
##### MSC:
 26A33 Fractional derivatives and integrals (real functions) 34A08 Fractional differential equations
##### References:
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