Abstract: We discussed the existence and stability of solutions for a class of nonlinear Caputo-type fractional q-difference equations with nonlocal integrals and generalized anti-periodic boundary conditions. Firstly, by using the Banach contraction mapping principle, we gave proof of the existence and uniqueness of solutions to the boundary value problem. Secondly, we gave Ulam stability results for this problem. Finally, the validity of the obtained results was verified through an example.

Key words: Caputo-type fractional q-difference equation, generalized anti-periodic boundary condition, Hyers-Ulam stability, Banach contraction mapping principle