  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.
