Browsing by Author "Chorfi, Nejmeddine"

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Citation - WoS: 4
Citation - Scopus: 4
Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels
(Elsevier, 2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; 56389; Matematik
The 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 < phi < 2, as well as between 1 < phi < 3/2. 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 (del(Q)) (tau) 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 (del(Q)) (tau) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Citation - WoS: 4
Citation - Scopus: 3
Theoretical And Numerical Computations Of Convexity Analysis For Fractional Differences Using Lower Boundedness
(World Scientific Publ Co Pte Ltd, 2023) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Abdeljawad, Thabet; Al-Sarairah, Eman; Abdeljawad, Thabet; Chorfi, Nejmeddine; 56389; Matematik
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 del(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, ((CFR)(a)del(alpha)f)(t) and ((ABR)(a)del(alpha)f)(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 H-k,H-epsilon and M-k,M-epsilon. The decrease of these sets enables us to obtain the relationship between the negative lower bound of ((CFR)(a)del(alpha)f)(t) and the convexity of the function on a finite time set given by N-a+1(P) := {a + 1, a + 2,..., P}, for some P is an element of Na+1 := {a + 1, a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets H-k,H- is an element of and M-k,M- is an element of in certain regions of the solutions for different values of k and is an element of. 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.