Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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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.
About the F-N Approximation to Fractional Neutron Transport Equation in Slab Geometry
(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru; Kadem, Abdelouahab
The neutron transport denotes the study of the motions and interactions of neutrons with materials. In given applications we need to know where neutrons are in an apparatus, what direction they are moving, and how fast they are going. In this manuscript the Legendre polynomial approximation method F-N was applied to the one dimensional slab geometry neutron transport equation.
Euler-Lagrange Equatıons On Cantor Sets
(Amer Soc Mechanical Engineers, 2014) Baleanu, Dumitru; Yang, Xiao-Jun
In this manuscript, we investigated the Euler-Lagrange equations on Cantor sets within the local fractional operators. To illustrate the proposed method two examples are presented.
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.
Fractional one-dimensional transport equation within spectral method combined with modified adomian decomposition method
(Amer Soc Mechanical Engineers, 2010) Baleanu, Dumitru; Kadem, Abdelouahab
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.
Lagrangians With Linear Velocities Within Hilfer Fractional Derivative
(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru
Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer's generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.
On constrained systems within Caputo derivatives
(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru
The constraints systems play a very important role in physics and engineering. The fractional variational principles were successfully applied to control problems as well as to construct the phase space of a fractional dynamical system. In this paper the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase-space is analyzed. One system possessing two primary first class constraints is analyzed in detail.
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.

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