Mohammed, Pshtiwan OthmanSrivastava, Hari M.Baleanu, DumitruAl-Sarairah, EmanSahoo, Soubhagya KumarChorfi, Nejmeddine2024-03-202024-03-202023Mohammed, P. O., Srivastava, H. M., Baleanu, D., Al-Sarairah, E., Sahoo, S. K., & Chorfi, N. Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels. Journal of King Saud University - Science, 35(7), 102794. https://doi.org/10.1016/j.jksus.2023.102794https://doi.org/10.1016/j.jksus.2023.102794https://hdl.handle.net/1828/16236The 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<32. 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.enAttribution-NonCommercial-NoDerivatives 4.0 InternationalArticleDepartment of Mathematics and Statistics