Fractional integrals and derivatives in q-calculus

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On q–Analogues of Caputo Derivative and Mittag–Leffler Function (2007, background): “In [13] the next useful statement is proven.”
Caputo q-fractional initial value problems and a q-analogue Mittag–Leffler function (2011, methodology): “The following identity [13] is essential to solve linear q-fractional equations qI α a (x− a) μ q = Γq(μ+ 1) Γq(α+ μ+ 1) (x− a) q (0 < a < x < b) (46) where α ∈ R and μ ∈ (−1,∞).”
Certain subclasses of analytic functions associated with fractional q-calculus operators (2011, background): “One may refer to the book [7], and the recent papers [1], [6], [8] and [11] on the subject.”