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Existence and uniqueness of positive solution for nonlinear fractional q-difference equation with integral boundary conditions |
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| Authors: | Caixia Guo Jianmin Guo Shugui Kang Huapeng Li |
| Affiliation: | School of Mathematical and Statistics, Shanxi Datong University, Xingyun Street, 037009, Datong, China,School of Mathematical and Statistics, Shanxi Datong University, Xingyun Street, 037009, Datong, China,School of Mathematical and Statistics, Shanxi Datong University, Xingyun Street, 037009, Datong, China and School of Mathematical and Statistics, Shanxi Datong University, Xingyun Street, 037009, Datong, China |
| Abstract: | This paper studies a class of nonlinear fractional $q$-difference equations with integral boundary conditions. By exploiting the properties of Green"s function and two fixed point theorems for a sum operator, the existence and uniqueness of positive solutions for the boundary value problem are established. Iterative schemes for approximating the solutions are also obtained. Explicit examples are given to illustrate main results. |
| Keywords: | Fractional q-difference integral boundary value problem fixed point theorem positive solution. |
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