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2007 | 5 | 3 | 285-292
Tytuł artykułu

Gravitational potential in fractional space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by $$G_\alpha = \frac{{2\Gamma \left( {\frac{\alpha }{2}} \right)}}{{\pi ^{\alpha /2 - 1} (\alpha - 2)}}G$$ , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.
Wydawca

Czasopismo
Rocznik
Tom
5
Numer
3
Strony
285-292
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-04-12
Twórcy
autor
  • Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University, 06530, Ankara, Turkey, dumitru@cankaya.edu.tr
Bibliografia
  • [1] X. He: “Anisotropy and isotropy”, Solid State Commun., Vol. 75, (1990), pp. 111–114. http://dx.doi.org/10.1016/0038-1098(90)90352-C[Crossref]
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  • [3] C. Palmer and P.N. Stavrinou: “Equations of motions in a non-integer dimensional space”, J. Phys. A: Math. Gen., Vol. 37, (2004), pp. 6987–7003. http://dx.doi.org/10.1088/0305-4470/37/27/009[Crossref]
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  • [5] M.A. Lohe and A. Thilagam: “Quantum mechanical models in fractional dimensions”, J. Phys. A: Math. Gen., Vol. 37, (2004), pp. 6181–6199. http://dx.doi.org/10.1088/0305-4470/37/23/015[Crossref]
  • [6] A. Zeilinger, and K. Svozil: “Measuring the dimension of space-time”, Phys. Rev. Lett., Vol. 54, (1985), pp. 2553–2555; K. Svozil: “Quantum field theory on fractal space-time”, J. Phys. A: Math. Gen., Vol. 20, (1987), pp. 3861–3875. http://dx.doi.org/10.1103/PhysRevLett.54.2553[Crossref]
  • [7] K.G. Willson: “Quantum field theory, models in less than 4 dimensions”, Phys. Rev. D, Vol. 7, (1973), pp. 2911–2926. http://dx.doi.org/10.1103/PhysRevD.7.2911[Crossref]
  • [8] F.H. Stillinger: “Axiomatic basis for spaces with non-integer dimension”, J. Math. Phys., Vol. 18, (1977), pp. 1224–1234. http://dx.doi.org/10.1063/1.523395[Crossref]
  • [9] C.W. Misner, K.S. Thorne and J.A. Wheeler: Gravitation, Freeman, San Francisco, 1973.
  • [10] K.S. Miller and B. Ross: An Introduction to the Fractional Integrals and Derivatives-Theory and Applications, Gordon and Breach, Longhorne, PA, 1993.
  • [11] J.A. Tenreiro Machado, I.S. Jesus, A. Galhano and J.B. Cunha: “Fractional order electromagnetics”, Signal Processing, Vol. 86, (2006), pp. 2637–2644. http://dx.doi.org/10.1016/j.sigpro.2006.02.010[Crossref]
  • [12] I. Podlubny: Fractional Differential Equations, Academic Press, New York, 1999.
  • [13] R. Gorenflo, A. Vivoli and F. Mainardi: “Discrete and continuous random walk models for space-time fractional diffusion, “Nonlinear Dynamics”, Vol. 38, (2004), pp. 101–116. http://dx.doi.org/10.1007/s11071-004-3749-5[Crossref]
  • [14] F. Mainardi: “Fractional relaxation-oscillation and fractional diffusion-wave phenomena”, Chaos, Solitons and Fractals, Vol. 7, (1996), pp. 1461–1477. http://dx.doi.org/10.1016/0960-0779(95)00125-5[Crossref]
  • [15] O.P. Agrawal: “Formulation of Euler-Lagrange equations for fractional variational problems”, J. Math. Anal. Appl., Vol. 272, (2002), pp. 368–379. http://dx.doi.org/10.1016/S0022-247X(02)00180-4[Crossref]
  • [16] Eqab M. Rabei and T. Alhalholy: “Potentials of arbitrary forces with fractional derivatives”, Int. J. Theor. Phys. A, Vol. 19, (2004), pp. 3083–3092.
  • [17] S. Muslih and D. Baleanu: “Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives”, J. Math. Anal. Appl., Vol. 304, (2005), pp. 599–606. http://dx.doi.org/10.1016/j.jmaa.2004.09.043[Crossref]
  • [18] A.A. Rousan, E. Malkawi, E.M. Rabei and H. Widyan: “Application of fractional calculus to gravity”, Frac. Calc. Appl. Anal., Vol. 5, (2002), pp. 155–168.
  • [19] N. Engheta: “On fractional calculus and fractional multipoles in electromagnetism”, IEEE Transactions on Antennas and Propagation, Vol. 44, (1996), pp. 554–566. http://dx.doi.org/10.1109/8.489308[Crossref]
  • [20] N. Engheta: “On the role of fractional calculus in electromanetic theory”, IEEE Antennas and Propagation Magazine, Vol. 39, (1997), pp. 35–46; “Fractional paradigm in electromagnetic theory”, In: D.H. Werner and R. Mitra (Eds.): Frontiers in Electromagnetics, IEEE Press, New York, 2000. http://dx.doi.org/10.1109/74.632994[Crossref]
  • [21] N. Engheta: “Fractional paradigm in electromagnetic theory”, In: D.H. Werner and R. Mitra (Eds.): Frontiers in Elctromagnetics, IEEE Press, 2000, Chapter 12, pp. 523–552.
  • [22] A. Shafer and B. Miller: “Bounds of for the fractal dimension of space”, J. Phys. A: Math. Gen., Vol. 19, (1986), pp. 3891–3902. http://dx.doi.org/10.1088/0305-4470/19/18/034[Crossref]
  • [23] D. Baleanu and S. Muslih: “Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives”, Physica Scripta, Vol. 72, (2005), pp. 119–121. http://dx.doi.org/10.1238/Physica.Regular.072a00119[Crossref]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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