Recently,　fractional　q-difference　equations　on　infinite　intervals　have　attracted　much　attention　due　to　their　potential　applications　in　many　fields.　In　this　paper,　we　investigate　a　class　of　nonlinear　high-order　fractional　q-difference　equations　with　integral　boundary　conditions　on　infinite　intervals,　where　the　nonlinearity　contains　Riemann-Liouville　fractional　q-derivatives　of　different　orders　of　unknown　function.　By　means　of　Schaefer　fixed　point　theorem,　Leray-Schauder　nonlinear　alternative　and　Banach　contraction　mapping　principle,　we　acquire　the　existence　and　uniqueness　results　of　solutions.　Furthermore,　we　establish　the　Hyers-Ulam　stability　for　the　proposed　problem.　In　the　end,　several　concrete　examples　are　utilized　to　demonstrate　the　validity　of　main　results.