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Successive iterations for unique positive solution of a nonlinear fractional q-integral boundary value problem |
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| Authors: | Guotao Wang Zhanbing Bai and Lihong Zhang |
| Institution: | School of Mathematics and Computer Science, Shanxi Normal Universi- ty,Linfen, Shanxi 041004, China,College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China and School of Mathematics and Computer Science, Shanxi Normal Universi- ty,Linfen, Shanxi 041004, China |
| 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. |
| Keywords: | Fractional q-difference equation q-integral condition explicit iterative sequence hybrid monotone method |
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