We prove the existence and uniqueness of solutions for a $k$-dimensional system of multi-term fractional $q$-integro-differential equations via anti-periodic boundary conditions by using some well-known tools of fixed point technique such as Arzel\`{a}--Ascoli theorem. We firstly give the corresponding Green's function for the boundary value problem and some of its attributes. In addition to, we give a numeric method to verify the analysis for checking the existence of a solution of the system. Finally, an interesting example is presented to illustrate the results.
