Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Fractional Systems With Multi-Parameters Fractional Derivatives(Springer, 2025) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.Recently, a generalization of fractional variational formulations in terms of multiparameter fractional derivatives was introduced by Agrawal and Muslih. This treatment can be used to obtain the Lagrangian and Hamiltonian equations of motion. In this paper, we also extend our work to introduce the generalization of the formulation for constrained mechanical systems containing multi-parameter fractional derivatives. Three examples for regular and constrained fractional systems are analyzed. © The Author(s) 2025.Conference Object Fractional One-Dimensional Transport Equation Within Spectral Method Combined With Modified Adomian Decomposition Method(Amer Soc Mechanical Engineers, 2010) Baleanu, D.; Kadem, A.In this paper the Chebyshev polynomials technique combined with the modified Adomian decomposition method were applied to solve analytically the fractional transport equation in one-dimensional plane geometry. Copyright © 2009 by ASME.Conference Object Fractional Mechanics on the Extended Phase Space(Amer Soc Mechanical Engineers, 2010) Baleanu, D.; Muslih, S.I.; Khalili Golmankhaneh, A.K.; Khalili Golmankhaneh, A.K.; Rabei, E.M.; Golmankhaneh, Alireza K.Fractional calculus has gained a lot of importance and potential applications in several areas of science and engineering. The fractional dynamics and the fractional variational principles started to be used intensively as an alternative tool in order to describe the physical complex phenomena. In this paper we have discussed the fractional extension of the classical dynam ics. The fractional Hamiltonian is constructed and the fractional generalized Poisson 's brackets on the extended phase space is established. Copyright © 2009 by ASME.Editorial Introduction To the Special Issue on Mathematical Aspects of Computational Biology and Bioinformatics-II(Tech Science Press, 2025) Baleanu, D.; Pinto, C.M.A.; Kumar, S.Article Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse(Korean Mathematical Soc, 2023) Baleanu, Dumitru; Kandasamy, Banupriya; Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, VarshiniThe goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.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.Article 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.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: 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.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.