Browsing by Author "Al-Sarairah, Eman"

Now showing 1 - 5 of 5

Citation - WoS: 3
Citation - Scopus: 3
Monotonicity and Extremality Analysis of Difference Operators in Riemann-Liouville Family
(Amer inst Mathematical Sciences-aims, 2023) Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; Mohammed, Pshtiwan Othman; Baleanu, Dumitru
In this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on Nr0+1, respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be obtained in view of these results combined with another condition (see Theorems 2.1 and 2.2). We will modify and reform the main two lemmas by replacing the main condition with a new simpler and stronger condition. For these new sufficient for the function to be monotone decreasing or increasing.
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) Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman
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: 8
Citation - Scopus: 8
On Convexity Analysis for Discrete Delta Riemann-Liouville Fractional Differences Analytically and Numerically
(Springer, 2023) Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann-Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the delta(2), which will be useful to obtain the convexity results. We examine the correlation between the positivity of ((RL)(w0)delta(alpha)f)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2, 3), H(k,E )and M-k,M-E. The decrease of these sets allows us to obtain the relationship between the negative lower bound of ((RL)(w0)delta(alpha)f)(t) and convexity of the function on a finite time set N-w0(P) := {w(0), w(0) + 1, w(0) + 2, ,P}for some P is an element of N-w0 := {w(0), w(0) + 1, w(0 )+ 2,...}. The numerical part of the paper is dedicated to examinin the validity of the setsH(k,E)and M-k,M-E for different values of k and E. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.
Citation - WoS: 6
Citation - Scopus: 6
A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting
(Mdpi, 2023) Mohammed, Pshtiwan Othman; Guirao, Juan Luis G.; Baleanu, Dumitru; Al-Sarairah, Eman; Jan, Rashid; Srivastava, Hari Mohan
The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville-Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions ((LC)(a)delta(mu)f) (a + J(0) + 1 - mu) >= (1 - mu)f(a + J(0))and ((LC)(a)delta(mu)f) (a + J(0) + 1 -mu) <= (1 - mu)f (a + J(0)) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results.
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) Al-Sarairah, Eman; Abdeljawad, Thabet; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman; Baleanu, Dumitru
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.