The solution theory for the fractional hybrid q-difference equations

This article discusses some basic properties of solutions to fractional hybrid q-difference equations. First, the existence theorem is presented by applying a fixed point theorem. Then, the stability result is derived by establishing a q-Gronwall inequality. This stability result also implies the uniqueness of the solution. Finally, a simple example is given to illustrate the effectiveness of our main results. Some conclusions in the literature are extended greatly.