Abdeljawad, ThabetBaleanu, Dumitru2019-12-162025-09-182019-12-162025-09-182017Abdeljawad, Thabet; Baleanu, Dumitru (2017). Monotonicity results for fractional difference operators with discrete exponential kernels, Advances in Difference Equations.1687-1847https://doi.org/10.1186/s13662-017-1126-1https://hdl.handle.net/20.500.12416/14650Abdeljawad, Thabet/0000-0002-8889-3768We 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.eninfo:eu-repo/semantics/openAccessDiscrete Exponential KernelCaputo Fractional DifferenceRiemann Fractional DifferenceDiscrete Fractional Mean Value TheoremArticle10.1186/s13662-017-1126-12-s2.0-85022232038