Browsing by Author "Hamed, Y. S."

Now showing 1 - 4 of 4

Citation Count: El-Zahar, Essam R...et al. (2020). "Absolutely stable difference scheme for a general class of singular perturbation problems", Advances in Difference Equations, vol. 2020, No. 1.
Absolutely stable difference scheme for a general class of singular perturbation problems
(2020) El-Zahar, Essam R.; Alotaibi, A. M.; Ebaid, Abdelhalim; Baleanu, Dumitru; Machado, Jose Tenreiro; Hamed, Y. S.; 56389
This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem is approximated by a first-order delay differential equation with a variable deviating argument. This delay differential equation is transformed into a three-term difference equation that can be solved using the Thomas algorithm. The uniqueness and stability analysis are discussed, showing that the method is absolutely stable. An optimal estimate for the deviating argument is obtained to take advantage of the second-order accuracy of the central finite difference method in addition to the absolute stability property. Several problems having left, right, interior, or twin boundary layers are considered to validate and illustrate the method. The numerical results confirm that the deviating argument can stabilize the unstable discretized differential equation and that the new approach is effective in solving the considered class of singular perturbation problems.
Citation Count: Zhou, Shuang-Shuang...et al. (2021). "Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function", AIMS Mathematics, Vol. 6, no. 8, pp. 8001-8029.
Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function
(2021) Zhou, Shuang-Shuang; Rashid, Saima; Rauf, Asia; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; 234808
In this paper, we propose a new framework of weighted generalized proportional fractional integral operator with respect to a monotone function psi; we develop novel modifications of the aforesaid operator. Moreover, contemplating the so-called operator, we determine several notable weighted Chebyshev and Gruss type inequalities with respect to increasing, positive and monotone functions psi by employing traditional and forthright inequalities. Furthermore, we demonstrate the applications of the new operator with numerous integral inequalities by inducing assumptions on ! and psi verified the superiority of the suggested scheme in terms of e fficiency. Additionally, our consequences have a potential association with the previous results. The computations of the proposed scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.
Citation Count: Rashid, Saima...et al. (2021). "Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application", CHAOS SOLITONS & FRACTALS, Vol. 151.
Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application
(2021) Rashid, Saima; Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; 234808
Discrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain (h) over barZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABTL), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having (h) over bar -discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Polya-Szego and Chebyshev type inequalities introduced within discrete AB-fractional operators having h-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated. (C) 2021 Elsevier Ltd. All rights reserved.
Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2022). "Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types", Electronic Research Archive, Vol.30, No.8, pp.3058-3070.
Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types
(2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; 56389
In this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.