Browsing by Author "Al-Sarairah, Eman"

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Citation Count: Srivastava, Hari Mohan...et.al. (2023). "A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting", Symmetry-Basel, Vol.15, No.2.
A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting
(2023) Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Guirao, Juan Luis G.; Baleanu, Dumitru; Al-Sarairah, Eman; Jan, Rashid; : 56389
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 Count: Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and extremality analysis of difference operators in Riemann-Liouville family", AIMS Mathematics, Vol.8, No.3, pp.5303-5317.
Monotonicity and extremality analysis of difference operators in Riemann-Liouville family
(2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y.S.; 56389
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 lemmas, we will establish similar results related to the relative minimum and relative maximum again. Finally, some examples, figures and tables are reported to demonstrate the applicability of the main lemmas. Furthermore, we will clarify that the first condition in the main first two lemmas is solely not sufficient for the function to be monotone decreasing or increasing.
Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels", Journal of King Saud University - Science, Vol35, No.7.
Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels
(2023) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; 56389
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<φ<2, as well as between 1<φ<[Formula presented]. 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.
Citation Count: Baleanu, D.;...et.al. (2023). "On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically", Journal of Inequalities and Applications, Vol.2023, no.1.
On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically
(2023) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y.S.; 56389
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 Δ 2, which will be useful to obtain the convexity results. We examine the correlation between the positivity of (w0RLΔαf)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2 , 3 ) , Hk,ϵ and Mk,ϵ. The decrease of these sets allows us to obtain the relationship between the negative lower bound of (w0RLΔαf)(t) and convexity of the function on a finite time set Nw0P:={w0,w0+1,w0+2,…,P} for some P∈Nw0:={w0,w0+1,w0+2,…}. The numerical part of the paper is dedicated to examinin the validity of the sets Hk,ϵ and Mk,ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.
Citation Count: Mohammed, Pshtiwan Othman ;...et.al. (2023). "Theoretıcal And Numerıcal Computatıons Of Convexıty Analysıs For Fractıonal Dıfferences Usıng Lower Boundedness", Fractals, Vol.31, No.8.
Theoretical And Numerical Computations Of Convexity Analysis For Fractional Differences Using Lower Boundedness
(2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Al-Sarairah, Eman; Abdeljawad, Thabet; 56389
his 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.