Abstract
In this paper, by applying the cone theory in ordered Banach spaces associated with the characters of increasing $$\varphi -(h,e)$$ -concave operators, we investigate the existence and uniqueness of nontrivial solutions for a nonlinear fractional q-difference equation boundary value problem. The main results show that we can construct an iterative scheme approximating the unique nontrivial solution. Relying on an example, we show the efficiency and applicability of the main result.
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