Abstract
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 .
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S.I. Muslih, on leave of absence from Al-Azhar University Gaza.
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Sadallah, M., Muslih, S.I. Solution of the Equations of Motion for Einstein’s Field in Fractional D Dimensional Space-Time. Int J Theor Phys 48, 3312 (2009). https://doi.org/10.1007/s10773-009-0133-8
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DOI: https://doi.org/10.1007/s10773-009-0133-8