WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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.Conference Object Citation - WoS: 29Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics(Springer international Publishing Ag, 2019) Yang, Xiao-Jun; Gao, Feng; Machado, J. A. Tenreiro; Baleanu, DumitruEditorial Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, BashirArticle 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 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 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.Book Part Citation - WoS: 25Citation - Scopus: 1New Treatise in Fractional Dynamics(Springer-verlag Berlin, 2012) Baleanu, Dumitru; Baleanu, DumitruFractional calculus becomes a powerful tool used to investigate complex phenomena from various fields of science and engineering. In this context, the researchers paid a lot of attention for the fractional dynamics. However, the fractional modeling is still at the beginning of its developing. The aim of this chapter is to present some new results in the area of fractional dynamics and its applications.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.Conference Object Citation - WoS: 2Citation - Scopus: 2Difference Discrete Variational Principles(Amer inst Physics, 2006) Baleanu, Dumitru; Jarad, FahdThe paper provides the discrete Lagrangian and Hamiltonian formulations of mechanical systems for both non-singular and singular cases. The Lagrangians with linear velocities and with higher velocities are investigated and the corresponding difference Euler-Lagrange equations and Hamiltonians are found.