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Browsing Matematik Bölümü by Institution Author "Baleanu, Dumitru"
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Article Citation - WoS: 64Citation - Scopus: 70About Fractional Quantization and Fractional Variational Principles(Elsevier, 2009) Baleanu, Dumitruin this paper, a new method of finding the fractional Euler-Lagrange equations within Caputo derivative is proposed by making use of the fractional generalization of the classical Fad di Bruno formula. The fractional Euler-Lagrange and the fractional Hamilton equations are obtained within the 1 + 1 field formalism. One illustrative example is analyzed. (C) 2008 Elsevier B.V. All rights reserved.Editorial Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology Preface(intech Europe, 2012) Baleanu, Dumitru; Baleanu, Dumitru; MatematikArticle Citation - WoS: 19Citation - Scopus: 23Comments On: "the Failure of Certain Fractional Calculus Operators in Two Physical Models(Walter de Gruyter Gmbh, 2020) Baleanu, DumitruIn these comments, I analyse the results reported by Ortigueira et al. [18] regarding the potential applications of non-singular fractional operators suggested by Caputo-Fabrizio and Atangana-Baleanu. My purpose is to show that the opinions of [18] are not consistent.Article Citation - WoS: 4Citation - Scopus: 4Cosmological Perturbations in Frw Model With Scalar Field Within Hamilton-Jacobi Formalism and Symplectic Projector Method(Sciendo, 2006) Baleanu, DumitruThe Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed. (c) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.Conference Object Citation - WoS: 21Citation - Scopus: 27Fractional Constrained Systems and Caputo Derivatives(Asme, 2008) Baleanu, DumitruDuring the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system. Based on the Caputo derivatives, the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase space is discussed. Two examples of discrete constrained system are analyzed in detail.Article Citation - WoS: 53Citation - Scopus: 59Fractional Hamiltonian Analysis of Irregular Systems(Elsevier, 2006) Baleanu, DumitruThe fractional Hamiltonian systems with linearly dependent constraints are investigated within fractional Riemann-Liouville derivatives. One example is analyzed in details and the consistency of fractional Euter-Lagrange and Hamilton equations is examined. (c) 2006 Elsevier B.V. All rights reserved.Article Citation - WoS: 31Citation - Scopus: 44Fractional Variational Principles in Action(Iop Publishing Ltd, 2009) Baleanu, DumitruThe fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational principles area. Therefore, the fractional Euler-Lagrange and Hamilton equations started to be examined intensely during the last decade. In this paper, we review some new trends in this field and we discuss some of their potential applications.Conference Object Citation - WoS: 50Citation - Scopus: 60New Applications of Fractional Variational Principles(Pergamon-elsevier Science Ltd, 2008) Baleanu, DumitruIn this paper the fractional variational principles of constrained systems involving Riesz derivatives are discussed and one example is analyzed in detail. The fractional Euler-Lagrange equations of two fractional Lagrangians which differ by a fractional Riesz derivative are investigated.Conference Object Citation - WoS: 7Citation - Scopus: 7Nonconservative Systems Within Fractional Generalized Derivatives(Sage Publications Ltd, 2008) Baleanu, DumitruA fractional derivative generalizes an ordinary derivative, and therefore the derivative of the product of two functions differs from that for the classical ( integer) case ; the integration by parts for Riemann-Liouville fractional derivatives involves both the left and right fractional derivatives. Despite these restrictions, fractional calculus models are good candidates for description of nonconservative systems. In this article, nonconservative Lagrangian mechanics are investigated within the fractional generalized derivative approach. The fractional Euler-Lagrange equations based on the Riemann-Liouville fractional derivatives are briefly presented. Using generalized fractional derivatives, we give a meaning for the term which appears in fractional Euler-Lagrange equations and contains the second order fractional derivative. The fractional Lagrangians and Hamiltonians of two illustrative nonconservative mechanical systems are investigated in detail.Conference Object Citation - Scopus: 1Solutions of a Fractional Dirac Equation(2010) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.This is a short version of a paper on the solution of a Fractional Dirac Equation (FDE). In this paper, we present two different techniques to obtain a new FDE. The first technique is based on a Fractional Variational Principle (FVP). For completeness and ease in the discussion to follow, we briefly describe the fractional Euler-Lagrange equations, and define a new Lagrangian Density Function to obtain the desired FDE. The second technique we define a new Fractional Klein-Gordon Equation (FKGE) in terms of fractional operators and fractional momenta, and use this equation to obtain the FDE. Our FDE could be of any order. We present eigensolutions for the FDE which are very similar to those for the regular Dirac equation. We give only a brief exposition of the topics here. An extended version of this work will be presented elsewhere. Copyright © 2009 by ASME.Editorial Citation - WoS: 2Citation - Scopus: 2
