Mohammed, Pshtiwan OthmanSrivastava, Hari MohanBaleanu, DumitruAl-Sarairah, EmanSahoo, Soubhagya KumarChorfi, Nejmeddine2024-01-122024-01-122023Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels", Journal of King Saud University - Science, Vol35, No.7.10183647http://hdl.handle.net/20.500.12416/6876The discrete analysed fractional operator technique was employed to demonstrate positive findings concerning the Atangana-Baleanu and discrete Caputo-Fabrizo fractional operators. Our tests utilized discrete fractional operators with orders between 1<φ<2, as well as between 1<φ<[Formula presented]. We employed the initial values of Mittag–Leffler functions and applied the principle of mathematical induction to ensure the positivity of the discrete fractional operators at each time step. As a result, we observed a significant impact of the positivity of these operators on ∇Q(τ) within Np0+1 according to the Riemann–Liouville interpretation. Furthermore, we established a correlation between the discrete fractional operators based on the Liouville-Caputo and Riemann–Liouville definitions. In addition, we emphasized the positivity of ∇Q(τ) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.eninfo:eu-repo/semantics/openAccessDiscrete Atangana-Baleanu Fractional OperatorsDiscrete Caputo-Fabrizo OperatorsDiscrete Fractional CalculusMonotonicity And PositivityArticle35710.1016/j.jksus.2023.102794