Mohammed, Pshtiwan OthmanSrivastava, Hari MohanBaleanu, DumitruElattar, Ehab E.Hamed, Y. S.2024-05-082024-05-082022Mohammed, Pshtiwan Othman;...et.al. (2022). "Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types", Electronic Research Archive, Vol.30, No.8, pp.3058-3070.2688-1594http://hdl.handle.net/20.500.12416/8174In this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.eninfo:eu-repo/semantics/openAccessDiscrete Fractional CalculusDiscrete Riemann-Liouville OperatorsDiscrete Liouville-Caputo Fractional OperatorsMonotonicity And PositivityArticle3083058307010.3934/era.2022155