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Successive iteration and positive solutions for boundary value problem of nonlinear fractional \(q\)-difference equation. (English) Zbl 1296.39003

Summary: In this paper, we investigate the positive solutions for a class of nonlinear \(q\)-fractional boundary value problem. We not only obtain the existence and uniqueness of positive solutions, but also establish the iterative schemes for approximating the solutions, which is benefit for computation and application.

MSC:

39A12 Discrete version of topics in analysis
34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
39A05 General theory of difference equations
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