Mohammed, Pshtiwan OthmanBaleanu, DumitruAl-Sarairah, EmanAbdeljawad, Thabet2024-01-242024-01-242023Mohammed, Pshtiwan Othman ;...et.al. (2023). "Theoretıcal And Numerıcal Computatıons Of Convexıty Analysıs For Fractıonal Dıfferences Usıng Lower Boundedness", Fractals, Vol.31, No.8.0218348Xhttp://hdl.handle.net/20.500.12416/6968his study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for ∇2 of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity and negativity of both of the discrete fractional differences, [Formula presented], with the convexity of the functions will be examined. In light of the main lemmas, we will define the two decreasing subsets of (2, 3), namely [Formula presented] and [Formula presented]. The decrease of these sets enables us to obtain the relationship between the negative lower bound of [Formula presented] and the convexity of the function on a finite time set given by [Formula presented], for some [Formula presented]. Besides, the numerical part of the paper is dedicated to examine the validity of the sets [Formula presented] and [Formula presented] in certain regions of the solutions for different values of k and [Formula presented]. For this reason, we will illustrate the domain of the solutions by means of several figures in which the validity of the main theorems are explained.eninfo:eu-repo/semantics/closedAccessAB and CF Fractional DifferencesConvexity AnalysisNegative and Nonnegative Lower BoundsNumerical ResultsTheoreticalArticle31810.1142/S0218348X23401837