In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by $$G_\alpha = \frac{{2\Gamma \left( {\frac{\alpha }{2}} \right)}}{{\pi ^{\alpha /2 - 1} (\alpha - 2)}}G$$ , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.
The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
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