TY - JOUR
T1 - THEORETICAL AND NUMERICAL COMPUTATIONS OF CONVEXITY ANALYSIS FOR FRACTIONAL DIFFERENCES USING LOWER BOUNDEDNESS
AU - Mohammed, Pshtiwan Othman
AU - Baleanu, Dumitru
AU - Al-Sarairah, Eman
AU - Abdeljawad, Thabet
AU - Chorfi, Nejmeddine
N1 - Publisher Copyright:
© 2023 The Author(s). The Author(s).
PY - 2023
Y1 - 2023
N2 - This 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, (aCFRαf)(t)and(aABRαf)(t), 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 k, and k,. The decrease of these sets enables us to obtain the relationship between the negative lower bound of αf)(t) and the convexity of the function on a finite time set given by Na+1P:= {a + 1,a + 2,...,P}, for some P Na+1:= {a + 1,a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets k, and k, in certain regions of the solutions for different values of k and k. 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.
AB - This 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, (aCFRαf)(t)and(aABRαf)(t), 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 k, and k,. The decrease of these sets enables us to obtain the relationship between the negative lower bound of αf)(t) and the convexity of the function on a finite time set given by Na+1P:= {a + 1,a + 2,...,P}, for some P Na+1:= {a + 1,a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets k, and k, in certain regions of the solutions for different values of k and k. 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.
KW - AB and CF Fractional Differences
KW - Convexity Analysis
KW - Negative and Nonnegative Lower Bounds
KW - Theoretical and Numerical Results
UR - http://www.scopus.com/inward/record.url?scp=85170219338&partnerID=8YFLogxK
U2 - 10.1142/S0218348X23401837
DO - 10.1142/S0218348X23401837
M3 - Article
AN - SCOPUS:85170219338
SN - 0218-348X
JO - Fractals
JF - Fractals
M1 - 2340183
ER -