Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions

Abstract We investigate the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions. Our results are based on some classical fixed point theorems. An illustrative example is also presented.

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