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    Citation Count: Abdeljawad, Thabet; Baleanu, Dumitru (2017). Monotonicity results for fractional difference operators with discrete exponential kernels, Advances in Difference Equations.
    Monotonicity results for fractional difference operators with discrete exponential kernels
    (Springer International Publishing AG, 2017-03-09) Abdeljawad, Thabet; Baleanu, Dumitru; 56389; 143529; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik - Bilgisayar Bölümü
    We prove that if the Caputo-Fabrizio nabla fractional difference operator ((CFR) (a-1)del(alpha) y)(t) of order 0 < alpha <= 1 and starting at a -1 is positive for t = a, a + 1,..., then y(t) is a-increasing. Conversely, if y(t) is increasing and y(a) >= 0, then ((CFR) (a-1)del(alpha)y)(t) >= 0. A monotonicity result for the Caputo-type fractional difference operator is proved as well. As an application, we prove a fractional difference version of the mean-value theorem and make a comparison to the classical discrete fractional case.