Physics
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009ijtp...48.3312s&link_type=abstract
International Journal of Theoretical Physics, Volume 48, Issue 12, pp.3312-3318
Physics
2
Conformal Scalar Field, Einstein’S Universe, Fractional Space
Scientific paper
As a continuation of Sadallah et al. work (M. Sadallah, S. Muslih and D. Baleanu, Equations of motion for Einstein’s field in non-integer dimensional space. Czechoslov. J. Phys. 56:323, 2006), the fractional action function S is given as an integration over fractional spatial dimension D s and fractional time D t dimension. The variational principle which minimize S leads to Euler-Lagrange equations of motion in D s + D t fractional dimensions. As an example we extend our study to obtain the equations of motion for Einstein’s field in fractional D s + D t fractional dimensions of N+1 space-time coordinates. It is shown that the time dependent solutions are single valued for only D s =4 dimensional space. Also the angular solutions are convergent for any value of D s .
Muslih Sami I.
Sadallah Madhat
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