Solution of the Equations of Motion for Einstein’s Field in Fractional <Emphasis Type="Italic">D</Emphasis> Dimensional Space-Time

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 .