文章基本信息

标题：Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives
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作者：Hojjat Afshari ; Mojtaba Sajjadmanesh ; Dumitru Baleanu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-18
DOI：10.1186/s13662-020-02568-2
出版社：Hindawi Publishing Corporation
摘要：In this paper we study the existence of unique positive solutions for the following coupled system: $$\begin{aligned} \textstyle\begin{cases} D_{0^{+}}^{\alpha }x(\tau )+f_{1}(\tau ,x(\tau ),D_{0^{+}}^{\eta }x( \tau ))+g_{1}(\tau ,y(\tau ))=0, \\ D_{0^{+}}^{\beta }y(\tau )+f_{2}(\tau ,y(\tau ),D_{0^{+}}^{\gamma }y( \tau ))+g_{2}(\tau ,x(\tau ))=0, \\ \tau \in (0,1),\qquad n-13$ and $1\leq \gamma \leq \xi \leq n-2$, $1\leq \eta \leq \zeta \leq n-2$, $f_{1},f_{2}:[0,1]\times \mathbb{R^{+}}\times \mathbb{R^{+}} \rightarrow \mathbb{R^{+}}$, $g_{1},g_{2}:[0,1]\times \mathbb{R^{+}}\rightarrow \mathbb{R^{+}}$ and $k_{1},k_{2}:\mathbb{R^{+}}\rightarrow \mathbb{R^{+}}$ are continuous functions, $D_{0^{+}}^{\alpha }$ and $D_{0^{+}}^{\beta }$ stand for the Riemann–Liouville derivatives. An illustrative example is given to show the effectiveness of theoretical results.
关键词：Fractional differential equation ; Mixed monotone operator ; Normal cone ; Coupled system ;