| Volume 9, Number 4, 2019, Pages 1204-1215 DOI：10.11948/2156-907X.20180193 |
| 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. |
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