Fractal Space Time and Variation of Fine Structure Constant

The effect of fractal space time of the quantum particles on the variation of the fine structure constant $\alpha$ has been studied. The variation of fine structure constant has been investigated around De Broglie length $\lambda$ and compton length $\lambda_{c}$ and it has been suggested that the variation may be attributed to the dimensional transition of the particle trajectories between these two quantum domains. Considering the Fractal universe with a small inhomogeneity in the mass distribution in the early universe, the variation of the fine structure constant have been investigated between matter and radiation dominated era. The fine structure constant shows a critical behaviour with critical exponent which is fractional and shows a discontinuity. It has been suggested that the variation of the fine structure constant may be attributed to the intrinsic scale dependance of the fundamental constants of nature.