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: 18Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel(Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, DumitruIn this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.Article Citation - WoS: 4Citation - Scopus: 2Symmetrically Substituted Zinc Phthalocyanine Derivatives Bearing N-Heterocycle Moieties Synthesis and Structural Analysis Investigations(Chiminform Data S A, 2014) Youssef, Tamer E.; Al-Turaif, Hamad; Baleanu, DumitruZinc(II)phthalocyanines bearing N-heterocycle moieties units were synthesized and characterized. Their Fourier transform infrared spectroscopic data were compared in order to characterize the investigated spectra. Fuzzy C-Means clustering technique was applied to extract some new information about these data. Hay synthesis of a novel series of symmetrically substituted zinc phthalocyanine derivatives, [(heteroxy)(8)ZnPcs] 4(a-e) bearing N-heterocycle moieties, i.e. Imidazol, Thiazol, Piperazine and Tetrazol rings, was reported. Their novel heterocycle-axyphthalonitrile precursors 3(a-e) were synthesized by the aromatic nucleophilic substitution reaction of 4,5-dichlorophthalonitrile with hetero-substituted phenols 2(a-e). The structure of the compounds was revealed by the spectroscopic analysis tools, in addition some hidden similarities of the raw spectra were revealed within the Fuzzy C-Means clustering technique.Conference Object On Fractional Hamilton Formulation Within Caputo Derivatives(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.Conference Object On Constrained Systems Within Caputo Derivatives(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Baleanu, DumitruThe constraints systems play a very important role in physics and engineering. The fractional variational principles were successfully applied to control problems as well as to construct the phase space of a fractional dynamical system. In this paper the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase-space is analyzed. One system possessing two primary first class constraints is analyzed in detail.Conference Object Citation - WoS: 5Citation - Scopus: 6Lagrangians With Linear Velocities Within Hilfer Fractional Derivative(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru; Agrawal, Om P.; Muslih, Sami I.Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer's generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.Conference Object Citation - Scopus: 3Euler-Lagrange Equations on Cantor Sets(Amer Soc Mechanical Engineers, 2014) Baleanu, Dumitru; Yang, Xiao-JunIn this manuscript, we investigated the Euler-Lagrange equations on Cantor sets within the local fractional operators. To illustrate the proposed method two examples are presented.Book Part Citation - WoS: 1Citation - Scopus: 1Cantor-Type Spherical-Coordinate Method for Differential Equations Within Local Fractional Derivatives(de Gruyter Open Ltd, 2015) Rahmat, Mohamad Rah Segi; Baleanu, Dumitru; Yang, Xiao-Jun; Segi Rahmat, Mohamad RafiIn this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.Article Citation - WoS: 9Citation - Scopus: 9A High-Accuracy Vieta-Fibonacci Collocation Scheme To Solve Linear Time-Fractional Telegraph Equations(Taylor & Francis Ltd, 2022) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, SoheilThe vital target of the current work is to construct two-variable Vieta-Fibonacci polynomials which are coupled with a matrix collocation method to solve the time-fractional telegraph equations. The emerged fractional derivative operators in these equations are in the Caputo sense. Telegraph equations arise in the fields of thermodynamics, hydrology, signal analysis, and diffusion process of chemicals. The orthogonality of derivatives of shifted Vieta-Fibonacci polynomials is proved. A bound of the approximation error is ascertained in a Vieta-Fibonacci-weighted Sobolev space that admits increasing the number of terms of the series solution leads to the decrease of the approximation error. The proposed scheme is implemented on four illustrated examples and obtained numerical results are compared with those reported in some existing research works.Article Citation - WoS: 29Citation - Scopus: 21A New Fractional Infectious Disease Model Under the Non-Singular Mittag-Leffler Derivative(Taylor & Francis Ltd, 2022) Liu, Xuan; Ur Rahmamn, Mati; Ahmad, Saeed; Baleanu, Dumitru; Nadeem Anjam, YasirIn this manuscript, we consider a fractional mathematical model, which describes the dynamics of infectious disease, under the non-singular Mittag-Leffler derivative. The model under consideration is the extension of the SIRV model, where the infectious class has been divided into two compartments, namely the acute and chronically infectious individuals. First, we obtain the possible equilibrium states of the given model. With the help of the next generation matrix approach, the reproduction number has been calculated for the system to find conditions on the spread or control of the disease. Additionally, a new concept of strength number and analysis of the second derivative of the Lyapunov function has been used for the detection of waves. We investigate the said problem for qualitative analysis and determine at least one solution by applying the approach of fixed point theory. For approximate solution, the technique of iterative fractional-order Adams-Bashforth scheme has been used. Numerical simulation for the proposed scheme has been performed at various fractional-order lying between 0, 1 and for integer-order 1. All the compartments show convergency and stability with growing time. A good comparative result has been given by different fractional orders and achieves stability faster at the low fractional orders.