WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 16Citation - Scopus: 23On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; MatematikThe fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.Article Citation - WoS: 88Citation - Scopus: 98On Fractional Euler-Lagrange and Hamilton Equations and the Fractional Generalization of Total Time Derivative(Springer, 2008) Muslih, Sami I.; Rabei, Eqab M.; Baleanu, DumitruFractional mechanics describe both conservative and nonconservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics, the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a given classical Lagrangian or by multiplying with a constant, the Lagrangian we obtain are the same equations of motion. In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann-Liouville fractional derivatives. As a consequence of applying this procedure, the classical results are reobtained as a special case. The fractional generalization of Faa di Bruno formula is used in order to obtain the concrete expression of the fractional Lagrangians which differs from a given fractional Lagrangian by adding a fractional derivative. The fractional Euler-Lagrange and Hamilton equations corresponding to the obtained fractional Lagrangians are investigated, and two examples are analyzed in detail.Conference Object Citation - WoS: 7Citation - Scopus: 7Nonconservative Systems Within Fractional Generalized Derivatives(Sage Publications Ltd, 2008) Baleanu, Dumitru; Muslih, Sami I.A 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.Article Citation - WoS: 2Citation - Scopus: 5Fractional Euler-Lagrange and Fractional Hamilton Equations for Super Symmetric Classical Model(World Scientific Publ Co Pte Ltd, 2007) Muslih, Sami I.; Baleanu, DumitruFractional Euler-Lagrange equations were investigated in the presence of the elements of Berezin algebra. The super fractional Hessian was defined and the fractional Hamiltonian of the super symmetric classical model was constructed.