Fractional relativity

By fractional relativity we mean a theoretical framework to study physics with the dispersion relation $E^{\alpha}=m^{\alpha}c^{2\alpha}+p^{\alpha}c^{\alpha}$, which recovers special relativity at $\alpha=2$. One such framework is established in a particular curved energy-momentum space. It is shown that the fractional Schr\"{o}dinger equation arises as a nonrelativistic limit of the Klein-Gordon equation in fractional relativity. In this framework, the relative locality makes no contribution to the position uncertainty at the classical level, and the Faraday's law in classical electrodynamics is modified by fractional derivatives.