Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order
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Authors
Mengru Hao
- School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China.
Chengbo Zhai
- School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, P.R. China.
Abstract
In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution
to a coupled system of fractional boundary value problems given by
\[
\begin{cases}
-D^{\nu_1}_{0^+}y_1(t) = \lambda_1a_1(t)f(t, y_1(t), y_2(t)) + e_1(t),\\
-D^{\nu_2}_{0^+}y_2(t) = \lambda_2a_2(t)g(t, y_1(t), y_2(t)) + e_2(t),
\end{cases}
\]
where \(\nu_1,\nu_2\in (n - 1; n]\) for \(n > 3\) and \(n \in N\), subject to the boundary conditions \(y^(i)_1 (0) = 0 = y^(i)_2 (0)\), for
\(0 \leq i \leq n - 2\), and \([D^{\alpha}_{0^+}y_1(t)]_{t=1}=0=[D^{\alpha}_{0^+}y_2(t)]_{t=1}\), for \(1 \leq\alpha\leq n - 2\).
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ISRP Style
Mengru Hao, Chengbo Zhai, Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 2, 131--137
AMA Style
Hao Mengru, Zhai Chengbo, Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order. J. Nonlinear Sci. Appl. (2014); 7(2):131--137
Chicago/Turabian Style
Hao, Mengru, Zhai, Chengbo. "Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order." Journal of Nonlinear Sciences and Applications, 7, no. 2 (2014): 131--137
Keywords
- Fractional differential equation
- Schauder fixed point theorem
- Positive solution.
MSC
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