Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 14Citation - Scopus: 15New Multi-Functional Approach for Κth-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, (h)over-Bar) Functions in Hilbert Space(World Scientific Publ Co Pte Ltd, 2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-MingThis work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex and approximately psi-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions such as higher-order strongly (HOS) generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions and HOS generalized psi-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized psi-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields.Article Citation - WoS: 5Citation - Scopus: 8Predictive Dynamical Modeling and Stability of the Equilibria in a Discrete Fractional Difference Covid-19 Epidemic Model(Elsevier, 2023) Rashid, Saima; Akdemir, Ahmet Ocak; Khalid, Aasma; Baleanu, Dumitru; Al-Sinan, Bushra R.; Elzibar, O. A. I.; Chu, Yu-MingThe SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelof technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.Article Citation - WoS: 3Citation - Scopus: 3The Refinement-Schemes Unified Algorithms for Certain Nth Order Linear and Nonlinear Differential Equations With a Set of Constraints(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Ejaz, Syeda TehminaWe first present a generalized class of binary interpolating refinement schemes and their properties. Then the refinement-schemes-based unified algorithms for the solution of certain nth order linear and nonlinear differential equations with a set of constraints are presented. Moreover, several algorithms based on the refinement schemes for solving differential equations are the special cases of our algorithms.Article Citation - WoS: 1Citation - Scopus: 1The Inequalities for the Analysis of a Class of Ternary Refinement Schemes(Amer inst Mathematical Sciences-aims, 2020) Ejaz, Syeda Tehmina; Baleanu, Dumitru; Chu, Yu-Ming; Mustafa, GhulamThe ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further these algebraic expressions contain only the coefficients used in the refinement rules of the ternary schemes.Article Citation - WoS: 70Citation - Scopus: 65On Polya-Szego and Cebysev Type Inequalities Via Generalized K-Fractional Integrals(Springer, 2020) Jarad, Fahd; Kalsom, Humaira; Chu, Yu-Ming; Rashid, Saima; Kalsoom, HumairaIn this paper, we introduce the generalized k-fractional integral in terms of a new parameter k > 0, present some new important inequalities of Polya-Szego and Cebysev types by use of the generalized k-fractional integral. Our consequences with this new integral operator have the abilities to implement the evaluation of many mathematical problems related to real world applications.Article Citation - WoS: 29Citation - Scopus: 37New Generalizations in the Sense of the Weighted Non-Singular Fractional Integral Operator(World Scientific Publ Co Pte Ltd, 2020) Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, SaimaIn this paper, we propose a new fractional operator which is based on the weight function for Atangana{Baleanu (AB)-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted AB-fractional integral. We aim to establish Minkowski and reverse Holder inequalities by employing weighted AB-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate.Article Citation - WoS: 49Citation - Scopus: 64New Estimates Considering the Generalized Proportional Hadamard Fractional Integral Operators(Springer, 2020) Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; Zhou, Shuang-ShuangIn the article, we describe the Gruss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.Article Citation - WoS: 17Citation - Scopus: 14New Estimates of Integral Inequalities Via Generalized Proportional Fractional Integral Operator With Respect To Another Function(World Scientific Publ Co Pte Ltd, 2020) Hammouch, Zakia; Jarad, Fahd; Chu, Yu-Ming; Rashid, SaimaIn this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function phi has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function phi are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature.Article Citation - WoS: 85Citation - Scopus: 108Inequalities by Means of Generalized Proportional Fractional Integral Operators With Respect To Another Function(Mdpi, 2019) Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; Rashid, SaimaIn this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Psi. The authors prove several inequalities for newly defined GPF-integral with respect to another function Psi. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Psi and the proportionality index sigma. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.Article Citation - WoS: 31Citation - Scopus: 27Generalized Trapezium-Type Inequalities in the Settings of Fractal Sets for Functions Having Generalized Convexity Property(Springer, 2020) Ashraf, Rehana; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Khan, Zareen A.In the paper, we extend some previous results dealing with the Hermite-Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalized convex and obtain several bounds and new results applicable to convex functions by using the generalized Holder and power-mean inequalities.As an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.