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Fractional derivatives generalization of Einstein’s field equations

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Abstract

In this paper we set up a fractional generalization of Einstein’s field equations based on fractional derivatives inside the geodesic action integral and obtained non-local fractional Einstein’s field equations. More specifically, the total derivative of any generalized coordinate is considered to take the special form \( D = D_{classical} + kD_{fractional} ,k \) is a real parameter, \( D_{classical} \) is the classical derivative operator and \( D_{fractional} \) is the modified left Riemann–Liouville fractional derivative operator so that the classical result of the calculus of variations is considered as a particular case. Many attractive astrophysical and cosmological solutions have been obtained and discussed in some details.

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Acknowledgments

The author would like to thank the Key Laboratory of Numerical Simulation of Sichuan Province for their financial support.

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Authors and Affiliations

  1. Key Laboratory of Numerical Simulation of Sichuan Province and College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, Sichuan, China

    A. R. El-Nabulsi

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  1. A. R. El-Nabulsi
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Correspondence to A. R. El-Nabulsi.

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El-Nabulsi, A.R. Fractional derivatives generalization of Einstein’s field equations. Indian J Phys 87, 195–200 (2013). https://doi.org/10.1007/s12648-012-0201-4

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