Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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.Conference Object Fractional Hamiltonian Analysis of Systems With Linear Velocities Within Hilfer Derivatives(2012) Agrawal, O.P.; Baleanu, D.During the last decade a huge interest was devoted to develop the fractional variational principles within various fractional derivatives and to connect them to important applications in various branches of science and engineering. On this line of taught in this manuscript we have investigated the Hamiltonian formulation corresponding to the Lagrangian with linear velocities within Hilfer fractional derivatives. © 2012 IEEE.