Browsing by Author "Hamed, Y. S."

Now showing 1 - 13 of 13

Citation - WoS: 1
Citation - Scopus: 1
Absolutely stable difference scheme for a general class of singular perturbation problems
(Springer, 2020) El-Zahar, Essam R.; Baleanu, Dumitru; Alotaibi, A. M.; Ebaid, Abdelhalim; Baleanu, Dumitru; Machado, Jose Tenreiro; Hamed, Y. S.; 56389; Matematik
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 - WoS: 7
Citation - Scopus: 8
Analytical and numerical negative boundedness of fractional differences with Mittag-Leffler kernel
(Amer inst Mathematical Sciences-aims, 2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Dahal, Rajendra; Goodrich, Christopher S.; Hamed, Y. S.; Baleanu, Dumitru; 56389; Matematik
We show that a class of fractional differences with Mittag-Leffler kernel can be negative and yet monotonicity information can still be deduced. Our results are complemented by numerical approximations. This adds to a growing body of literature illustrating that the sign of a fractional difference has a very complicated and subtle relationship to the underlying behavior of the function on which the fractional difference acts, regardless of the particular kernel used.
Citation - WoS: 0
Citation - Scopus: 0
Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; 56389; Matematik
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 14
Citation - Scopus: 12
Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function
(Amer inst Mathematical Sciences-aims, 2021) Zhou, Shuang-Shuang; Jarad, Fahd; Rashid, Saima; Rauf, Asia; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; 234808; Matematik
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 - WoS: 31
Citation - Scopus: 32
Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision-Making
(Wiley, 2022) Zulqarnain, Rana Muhammad; Jarad, Fahd; Siddique, Imran; Jarad, Fahd; Hamed, Y. S.; Abualnaja, Khadijah M.; Iampan, Aiyared; 234808; Matematik
The Pythagorean fuzzy soft set (PFSS) is the most proficient and manipulative leeway of the Pythagorean fuzzy set (PFS), which contracts with parameterized values of the alternatives. It is a generalized form of the intuitionistic fuzzy soft set (IFSS), which provides healthier and more accurate evaluations through decision-making (DM). The main determination of this research is to prolong the idea of Einstein's aggregation operators for PFSS. We introduce the Einstein operational laws for Pythagorean fuzzy soft numbers (PFSNs). Based on Einstein operational laws, we construct two novel aggregation operators (AOs) such as Pythagorean fuzzy soft Einstein-weighted averaging (PFSEWA) and Pythagorean fuzzy soft Einstein-weighted geometric (PFSEWG) operators. In addition, important possessions of proposed operators, such as idempotency, boundedness, and homogeneity, are discussed. Furthermore, to validate the practicability of the anticipated operators, a multiple attribute group decision-making (MAGDM) method is developed. We intend innovative AOs considering the Einstein norms for PFSS to elect the most subtle business. Pythagorean fuzzy soft numbers (PFSNs) support us to signify unclear data in real-world perception. Furthermore, a numerical description is planned to certify the efficacy and usability of the projected method in the DM practice. The recent approach's pragmatism, usefulness, and tractability are validated through comparative exploration with the support of some prevalent studies.
Citation - WoS: 7
Citation - Scopus: 7
Fractional integral inequalities for exponentially nonconvex functions and their applications
(Mdpi, 2021) Srivastava, Hari Mohan; Baleanu, Dumitru; Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y. S.; 56389; Matematik
In this paper, the authors define a new generic class of functions involving a certain modified Fox-Wright function. A useful identity using fractional integrals and this modified Fox-Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite-Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.
Citation - WoS: 1
Citation - Scopus: 1
Monotonicity and extremality analysis of difference operators in Riemann-Liouville family
(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; 56389; Matematik
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: 9
Citation - Scopus: 9
More efficient estimates via ℏ-discrete fractional calculus theory and applications
(Pergamon-elsevier Science Ltd, 2021) Rashid, Saima; Jarad, Fahd; Sultana, Sobia; Jarad, Fahd; Jafari, Hossein; Hamed, Y. S.; 234808; Matematik
Discrete fractional calculus (DFC) is continuously spreading in the engineering practice, neural networks, chaotic maps, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. First, we start with a novel discrete h-proportional fractional sum defined on the time scale hZ so as to give the premise to the more broad and complex structures, for example, the suitably accustomed transformations conjuring the property of observing the new chaotic behaviors of the logistic map. Here, we aim to present the novel discrete versions of Gruss and certain other associated variants by employing discrete h-proportional fractional sums are established. Moreover, several novel consequences are recaptured by the h-discrete fractional sums. The present study deals with the modification of Young, weighted-arithmetic and geometric mean formula by taking into account changes in the exponential function in the kernel represented by the parameters of the operator, varying delivery noted outcomes. In addition, two illustrative examples are apprehended to demonstrate the applicability and efficiency of the proposed technique. (C) 2021 Elsevier Ltd. All rights reserved.
Citation - WoS: 20
Citation - Scopus: 20
Novel aspects of discrete dynamical type inequalities within fractional operators having generalized (h)over-bar-discrete Mittag-Leffler kernels and application
(Pergamon-elsevier Science Ltd, 2021) Rashid, Saima; Jarad, Fahd; Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; 234808; Matematik
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 - WoS: 10
Citation - Scopus: 11
Novel numerical investigation of the fractional oncolytic effectiveness model with M1 virus via generalized fractional derivative with optimal criterion
(Elsevier, 2022) Rashid, Saima; Jarad, Fahd; Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y. S.; 234808; Matematik
Oncolytic virotherapy is an efficacious chemotherapeutic agent that addresses and eliminates cancerous tissues by employing recombinant infections. M1 is a spontaneously produced oncolytic alphavirus with exceptional specificity and powerful activity in individual malignancies. The objective of this paper is to develop and assess a novel fractional differential equation (FDEs)-based mathematical formalism that captures the mechanisms of oncogenic M1 immunotherapy. The aforesaid framework is demonstrated with the aid of persistence, originality, non-negativity, and stability of systems. Additionally, we also examine all conceivable steady states and the requirements that must exist for them to occur. We also investigate the global stability of these equilibria and the characteristics that induce them to be unstable. Furthermore, the Atangana- Baleanu fractional-order derivative is employed to generalize a treatment of the cancer model. This novel type of derivative furnishes us with vital understanding regarding parameters that are widely used in intricate mechanisms. The Picard-Lindelof approach is implemented to investigate the existence and uniqueness of solutions for the fractional cancer treatment system, and Picard's stability approach is used to address governing equations. The findings reveal that the system is more accurate when the fractional derivative is implemented, demonstrating that the behaviour of the cancer treatment can be interpreted when non-local phenomena are included in the system. Furthermore, numerical results for various configurations of the system are provided to exemplify the established simulation.
Citation - WoS: 7
Citation - Scopus: 7
On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically
(Springer, 2023) Baleanu, Dumitru; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; 56389; Matematik
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: 17
Citation - Scopus: 18
On the enhancement of thermal transport of Kerosene oil mixed TiO2and SiO2across Riga wedge ∗
(Elsevier, 2022) Yahya, Asmat Ullah; Jarad, Fahd; Siddique, Imran; Jarad, Fahd; Salamat, Nadeem; Abdal, Sohaib; Hamed, Y. S.; Hussain, Sajjad; 234808; Matematik
Efficient thermal transportation in compact heat density gadgets is a prevailing issue to be addressed. The flow of a mono nanofluid (SiO2/Kerosene oil) and hybrid nanofluid (TiO2 + SiO2/ Kerosene oil) is studied in context of Riga wedge. The basic purpose of this work pertains to improve thermal conductivity of base liquid with inclusions of nano-entities. The hybrid nanofluid flow over Riga wedge is new aspect of this work. The concentration of new species is assumed to constitute the base liquid to be non-Newtonian. The fundamental formulation of the concentration laws of mass, momentum and energy involve partial derivatives. The associated boundary conditions are taken in to account. Similarity variables are utilized to transform the leading set of equations into ordinary differential form. Shooting procedure combined with Runge-Kutta method is harnessed to attain numerical outcomes. The computational process is run in matlab script. It is seen that the velocity component f'(eta) goes upward with exceeding inputs of modified Hartmann number Mh and it slows down when non-dimensional material parameter alpha(h), takes large values. Also, Nusselt number - theta'(0) is enhanced with developing values of Eckert number Ec and Biot number B-i.
Citation - WoS: 8
Citation - Scopus: 8
Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; 56389; Matematik
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.