Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 60Citation - Scopus: 68Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; MatematikFractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.Article Citation - WoS: 14Citation - Scopus: 19On the Discrete Sumudu Transform(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; MatematikIn this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.Article Citation - WoS: 1Citation - Scopus: 1No-Regret and Low-Regret Control for a Weakly Coupled Abstract Hyperbolic System(Wiley, 2025) Louafi, Meriem; Messaoudi, Mohammed; Abdeljawad, Thabet; Jarad, FahdThis paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave-like phenomena and complexity, become even more challenging with weak coupling between subsystems. The study introduces no-regret and low-regret control strategies to handle missing information and achieve optimal performance. By deriving the Euler-Lagrange optimality system, it characterizes these control approaches in the context of weak coupling. Additionally, the paper establishes the existence and uniqueness of a no-regret and low-regret control, emphasizing the influence of uncertain coupling parameters. These findings are optimal control strategies for abstract weakly coupled hyperbolic systems under uncertainty. Finally, as highlighted in our conclusion, future research could explore integrating memory effects through fractional derivatives to improve the modeling of viscoelasticity, diffusion with memory, and wave damping.Article Citation - WoS: 1Citation - Scopus: 2Some Results for Two Classes of Two-Point Local Fractional Proportional Boundary Value Problems(Univ Nis, Fac Sci Math, 2023) Jarad, Fahd; Laadjal, Zaid; Abdeljawad, ThabetIn this paper, we consider two classes of boundary value problems in the frame of local proportional fractional derivatives. For both of these classes, we obtain the associated Green's functions and discuss their properties. Using these properties, we go about the uniqueness of the solutions. In addition, we establish Lyapunov-type and Hartman-Wintner-type inequalities and build sharp estimated for the unique solutions of the considered equations.Article Citation - WoS: 12Citation - Scopus: 13Transmission Dynamics of a Novel Fractional Model for the Marburg Virus and Recommended Actions(Springer Heidelberg, 2023) Baleanu, Dumitru; Kumar, Sachin; Singh, Jaskirat Pal; Abdeljawad, ThabetMarburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana-Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R-0 < 1, Castillo's method and the next-generation matrix are used to demonstrate the disease-free equilibrium's asymptotic global stability. When R-0 > 1, the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model's basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution's existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model's numerical simulations.Article Citation - WoS: 44Citation - Scopus: 66Fractional Variational Principles With Delay(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Maaraba, ThabetThe fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler Lagrange equations are obtained and one example is analyzed in detail.Article Citation - WoS: 5Citation - Scopus: 4Sharp Estimates of the Unique Solution for Two-Point Fractional Boundary Value Problems With Conformable Derivative(Wiley, 2024) Jarad, Fahd; Laadjal, Zaid; Abdeljawad, ThabetIn this work, we investigate the condition of the given interval which ensures the existence and uniqueness of solutions for two-point boundary value problems within conformable-type local fractional derivative. The method of analysis is obtained by the principle of contraction mapping. Furthermore, benefiting from calculating the integral of the Green's function, we are able to improve a recent result by obtaining a sharper lower bound for an eigenvalue problem. Two examples are presented to clarify the obtained results. Finally, we present an open problem for the interested reader.Article Citation - WoS: 13Citation - Scopus: 29Selection of an Effective Hand Sanitizer To Reduce Covid-19 Effects and Extension of Topsis Technique Based on Correlation Coefficient Under Neutrosophic Hypersoft Set(Wiley-hindawi, 2021) Ali, Rifaqat; Siddique, Imran; Jarad, Fahd; Abdeljawad, Thabet; Samad, Abdul; Zulqarnain, Rana Muhammad; Sermutlu, EmreCorrelation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to develop the concept and characteristics of CC and the weighted correlation coefficient (WCC) of NHSS. We also introduced some aggregation operators in the considered environment, which can help us establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) based on CC and WCC under NHSS. A decision-making strategy is established to solve multicriteria group decision-making (MCGDM) problems utilizing developed methodology. Moreover, the proposed method is utilized for the selection of an effective hand sanitizer during the COVID-19 pandemic to ensure the validity of the proposed approach. The practicality, effectivity, and flexibility of the current approach are proved through comparative analysis with the assistance of some existing studies.Article Citation - WoS: 94Citation - Scopus: 105On More General Forms of Proportional Fractional Operators(de Gruyter Poland Sp Z O O, 2020) Abdeljawad, Thabet; Jarad, Fahd; Alqudah, Manar A.In this article, more general types of fractional proportional integrals and derivatives are proposed. Some properties of these operators are discussed.Article Citation - WoS: 26Citation - Scopus: 32On a More General Fractional Integration by Parts Formulae and Applications(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, AbdonThe integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.
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