一类非线性Riemann-Liouville分数阶微分方程耦合系统的正解

Positive Solutions to a Coupled System of Nonlinear Riemann-Liouville Fractional Differential Equations

文章研究一类非线性Riemann-Liouville型分数阶微分方程耦合系统正解的存在性和唯一性.借助格林函数的性质,运用Leray-Schauder抉择理论和Banach压缩映射原理,得到了该耦合系统正解的存在性和唯一性的充分条件,并举例说明了定理的有效性.

In this paper,the existence and uniqueness of positive solutions for a class of coupled systems of nonlinear Riemann-Liouville fractional differential equations are studied.The existence and uniqueness of positive solutions were obtained by using the properties of the associated Green’s function and the nonlinear alternative of Leray-Schauder type and Banach contraction mapping principle.The validity of the theorem is illustrated by examples.