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 Successive iterations for unique positive solution of a nonlinear fractional q-integral boundary value problem Guotao Wang,Zhanbing Bai,Lihong Zhang Keywords:Fractional q-difference equation; q-integral condition; Explicit iterative sequence; Hybrid monotone method. Abstract: In this paper, under certain nonlinear growth conditions, we investigate the existence and successive iterations for the unique positive solution of a nonlinear fractional $q$-integral boundary problem by employing hybrid monotone method, which is a novel approach to nonlinear fractional $q$-difference equation. This paper not only proves the existence of the unique positive solution, but also gives some computable explicit hybrid iterative sequences approximating to the unique positive solution.