Muslih, S.I.Agrawal, O.P.Baleanu, D.02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2023-01-042025-09-182023-01-042025-09-182009Muslih, Sami I.; Agrawal, Om P.; Baleanu, Dumitru (2010). "Solutions of a fractional Dirac equation", Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, Vol. 4, No. PART B, pp. 1011-1014.9780791843253978079184898297807918450359780791846322978079185704597807918378499780791844137978079184505997807918548399780791846407https://doi.org/10.1115/DETC2009-86521Design Engineering Division and Computers in Engineering DivisionThis 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. © 2009 by ASME. © 2013 Elsevier B.V., All rights reserved.eninfo:eu-repo/semantics/closedAccessConference Object10.1115/DETC2009-865212-s2.0-82155173247