Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 7About Fractional Calculus of Singular Lagrangians(Fuji Technology Press Ltd, 2005) Baleanu, DumitruIn this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.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.Editorial Citation - WoS: 2Citation - Scopus: 2Article 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.