Browsing by Author "Muslih, S.I."

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Citation - WoS: 10
Citation - Scopus: 10
About Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives
(American Society of Mechanical Engineers, 2005) Baleanu, D.; Muslih, S.I.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, 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 Schrödinger equation is presented. Copyright © 2005 by ASME.
Citation - Scopus: 1
Fractional Lagrangian and Hamiltonian Mechanics With Memory
(De Gruyter, 2019) Muslih, S.I.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional variational principles are very important for science and engineering. Within this field of study, the fractional Lagrangian and Hamiltonian equations are challenging ones from the viewpoint of mathematics. During the last fifteen years, the field of fractional variational principles was continuously improved and developed. In this chapter, the fractional variational principles-with and without delay-will be briefly reviewed. Several illustrative examples from mechanics are presented. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Fractional Mechanics on the Extended Phase Space
(Amer Soc Mechanical Engineers, 2009) Baleanu, D.; Muslih, S.I.; Khalili Golmankhaneh, A.K.; Khalili Golmankhaneh, A.K.; Rabei, E.M.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2009 by ASME. © 2013 Elsevier B.V., All rights reserved.
Fractional Systems With Multi-Parameters Fractional Derivatives
(Springer, 2025) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently, a generalization of fractional variational formulations in terms of multiparameter fractional derivatives was introduced by Agrawal and Muslih. This treatment can be used to obtain the Lagrangian and Hamiltonian equations of motion. In this paper, we also extend our work to introduce the generalization of the formulation for constrained mechanical systems containing multi-parameter fractional derivatives. Three examples for regular and constrained fractional systems are analyzed. © The Author(s) 2025.
Nonconservative Systems Within Fractional Generalized Derivatives
(IFAC Secretariat, 2006) Baleanu, D.; Muslih, S.I.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional calculus is a promising tool for investigation of both conservative and non-conservative systems. Fractional Hamiltonian formulation represents an important problem of the fractional quantization. In this paper the nonconservative Lagrangian mechanics is investigated within fractional generalized derivative approach.
Path Integral Quantization of Brownian Motion as Mechanical Systems With Fractional Derivatives
(IFAC Secretariat, 2006) Rabei, E.M.; Baleanu, D.; Muslih, S.I.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the mechanical systems with fractional derivatives are studied by using fractional formalism. The path integral quantization of these system is constructed as an integration over the canonical phase space. The path integral quantization of a system with Brownian motion is carried out. Copyright 2006 IFAC.
Citation - Scopus: 2
Solutions of a Fractional Dirac Equation
(2009) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2009 by ASME. © 2013 Elsevier B.V., All rights reserved.