We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport measurements have been used to characterize locally gated bipolar graphene $p$-$n$-$p$ junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the $p$ and $n$ regions. These fractional plateaus, originating from chiral edge states equilibration at the $p$-$n$ interfaces, exhibit sensitivity to inter-edge backscattering which is found to be strong for some of the plateuas and much weaker for other plateaus. We use this effect to explore the role of backscattering and estimate disorder strength in our graphene devices.