Fractional illusion theory of space: Fractional gravitational field with fractional extra-dimensions

We construct a matter field theory in a fractional theory of a space endowed with fractional extra-dimensions. Some important consequences are revealed and discussed in some details. In particular, the possible variation of the gravitational constant with distance, the Schwarzschild black hole and the hierarchy problem are considered. A novel approach towards solving the gauge hierarchy problem without supersymmetry and without compact extra spacetime dimensions is introduced. The spacetime is endowed within our framework with one time direction and four spatial directions with fractional dimensions of total sum equal to 3.