一类具分数阶积分条件的分数阶微分方程组解的存在唯一性

Existence and Uniqueness of Solution of Boundary Value Problems for a Fractional Differential System with Fractional Integral Conditions

利用Banach压缩映射原理,研究一类具有分数阶积分条件的分数阶微分方程组边值问题,其非线性项包含Caputo型分数阶导数,得到了该问题等价的积分方程组的格林函数及存在唯一解的充分条件,并给出了应用实例.

Using Banach contraction mapping principle, the authors investigated a fractional differential system with fractional integral conditions,which involved the Caputo fractional derivative with nonlinear terms,and established Green’s function of an equivalent integral equation to the system and sufficient conditions for the existence and uniqueness of solution of the system.An example was given to illustrate the application of the result.