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.
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