一类具有分数阶积分条件的分数阶微分方程组边值问题的可解性

Solvability for Boundary Value Problem of a Class of Fractional Differential System with Fractional Integral Conditions

研究一类具有Riemann-Liouville分数阶积分条件的分数阶微分方程组边值问题,将该问题转化为等价的积分方程组,应用Leray-Schauder不动点定理和Banach压缩映像原理,结合一个分数阶形式的新不等式,获得了该问题解的存在性和唯一性结果,并给出一个应用实例.

A class of boundary value problem of fractional differential system with Rie- mann-Liouville fractional integral conditions is investigated,it can be reduced to the equiva- lent integral system. By using Leray-Schauder fixed point theory and Banach contraction mapping principle combined with a new inequality of fractional order form, some sufficient conditions on the existence and uniqueness of Solution for boundary value problems are estab- lished. A example is given to illustrate the application of the result.