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2010

Riemann-Liouville Fractional Einstein Field Equations

Munkhammar, Joakim

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In this paper we establish a fractional generalization of Einstein field equations based on the Riemann-Liouville fractional generalization of the ordinary differential operator $\partial_\mu$.

We show some elementary properties and prove that the field equations correspond to the regular Einstein field equations for the fractional order $\alpha = 1$.
In addition to this we show that the field theory is inherently non-local in this approach.
We also derive the linear field equations and show that they are a generalized version of the time fractional diffusion-wave equation.

Riemann-Liouville Fractional Einstein Field Equations · Around

Built on

A. Einstein, A Generalization of the Relativistic Theory of Gravitation, The Annals of Mathematics, Second Series, Vol. 46, No. 4, pp. 578-584, (1945)
1945
Earlier work this paper cites.
S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives: theory and applications
1993
Earlier work this paper cites.
F. Mainardi, The time fractional diffusion-wave equation
1995
Earlier work this paper cites.
L. Oparnica, Generalized fractional calculus with applications in mechanics
2001
Earlier work this paper cites.
N. Laskin, Fractional Schrödinger equation
2002
Earlier work this paper cites.
J. Munkhammar, Riemann-Liouville fractional derivatives and the Taylor-Riemann series
2004
Earlier work this paper cites.

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Then

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2007
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B. Mashhoon, Gravitoelectromagnetism: A Brief Review. arXiv:gr-qc/0311030v2 17 Apr 2008
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2009
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Original
2009
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