Browsing by Author "Hamed, Y.S."

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Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions
(2022) Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Hamed, Y.S.; Elattar, Ehab E.; 56389
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ( CFR c0 r∇F ) (t) > -ϵ λ(θ - 1) - rF ∇ (c0 + 1) such that - rF ∇ (c0 + 1) ≥ 0 and ϵ > 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 ϵ and θ.
Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision-Making
(2022) Jarad, Fahd; Siddique, Imran; Jarad, Fahd; Hamed, Y.S.; Abualnaja, Khadijah M.; Iampan, Aiyared; 234808
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.
Fractional integral inequalities for exponentially nonconvex functions and their applications
(2021) Baleanu, Dumitru; Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y.S.; 56389
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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Monotonicity and extremality analysis of difference operators in Riemann-Liouville family
(2023) Baleanu, Dumitru; Abdeljawad, Thabet; 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.
More efficient estimates via ℏ-discrete fractional calculus theory and applications
(2021) Jarad, Fahd; Sultana, Sobia; Jarad, Fahd; Jafari, Hossein; Hamed, Y.S.; 234808
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 ℏ-proportional fractional sum defined on the time scale ℏZ 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 Grüss and certain other associated variants by employing discrete ℏ-proportional fractional sums are established. Moreover, several novel consequences are recaptured by the ℏ-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. © 2021 Elsevier Ltd
Novel numerical investigation of the fractional oncolytic effectiveness model with M1 virus via generalized fractional derivative with optimal criterion
(2022) Jarad, Fahd; Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y.S.; 234808
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.
On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically
(2023) Baleanu, Dumitru; Abdeljawad, Thabet; 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.
On the enhancement of thermal transport of Kerosene oil mixed TiO2and SiO2across Riga wedge ∗
(2022) Jarad, Fahd; Siddique, Imran; Jarad, Fahd; Salamat, Nadeem; Abdal, Sohaib; Hamed, Y.S.; Abualnaja, Khadijah M.; Hussain, Sajjad; 234808
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′(η) goes upward with exceeding inputs of modified Hartmann number Mh and it slows down when non-dimensional material parameter αh takes large values. Also, Nusselt number - θ′(0) is enhanced with developing values of Eckert number Ec and Biot number Bi.