Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Publication About Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives(Amer Soc Mechanical Engineers, 2005) Baleanu, Dumitru; Muslih, Sami I.sRecently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal's approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schrodinger equation is presented.Publication 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.Publication Fractional mechanics on the extended phase space(Amer Soc Mechanical Engineers, 2010) Baleanu, Dumitru; Muslih, Sami I.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Rabei, Eqab M.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 dynamics. The fractional Hamiltonian is constructed and the fractional generalized Poisson's brackets on the extended phase space is established.