一类非线性Caputo型分数阶微分方程耦合系统解的存在性和稳定性

Existence and stability of coupled system solutions for a class of nonlinear Caputo-type fractional-order differential equations

研究一类非线性Caputo型分数阶微分方程耦合系统的边值问题。首先,将方程转化为等价的积分方程;其次,利用Leray-Schauder抉择和Banach压缩映像原理讨论该边值问题解的存在性和唯一性的充分条件;最后,分析该耦合系统的Ulam-Hyers、Ulam-Hyers-Rassias和Ulam-Hyers-Mittag-Leffer稳定性。

The boundary value problem of a class of coupled systems with nonlinear Caputo-type fractional differential equations is studied.Firstly,the equation is transformed into an equivalent integral equation.Secondly,the sufficient conditions for the existence and uniqueness of the solution of the boundary value problem are proved by Leray-Schauder choice and Banach compression mapping principle.Finally,the stability of Ulam-Hyers,Ulam-Hyers-Rassias and Ulam-Hyers-Mittag-Leffer of the coupling system is analyzed.