Existence of positive solutions for a coupled system of nonlinear fractional differential equations
We study the following nonlinear boundary-value problems for fractional differential equations $$D^{\alpha} u(t) = f(t, v(t),D^{\beta - 1}v(t)), t > 0,\\ D^{\beta} v(t) = g(t, u(t),D^{\alpha - 1}u(t)), t > 0,\\ u > 0,\; v > 0 \in (0,\infty), \lim_{t\rightarrow 0+} u(t) =...
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| Date: | 2019 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1417 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study the following nonlinear boundary-value problems for fractional differential equations
$$D^{\alpha} u(t) = f(t, v(t),D^{\beta - 1}v(t)), t > 0,\\
D^{\beta} v(t) = g(t, u(t),D^{\alpha - 1}u(t)), t > 0,\\
u > 0,\; v > 0 \in (0,\infty),
\lim_{t\rightarrow 0+}
u(t) = \lim_{t\rightarrow 0+}
v(t) = 0,$$
where $1 < \alpha \leq 2$ and $1 < \beta \leq 2$. Under certain conditions on $f$ and $g$, the existence of positive solutions is obtained by
applying the Schauder fixed-point theorem. |
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