Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order


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


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