一类具有分数阶积分条件的分数阶微分方程边值问题解的存在性

Existence of Solution for the Boundary Value Problem of a Class of Fractional Differential Equation with Fractional Integral Conditions

研究一类具有分数阶积分条件的分数阶微分方程边值问题,其非线性项包含Caputo型分数阶导数.将该问题转化为等价的积分方程,利用Leray-Schauder非线性抉择原理结合一个范数形式的新不等式,获得一定增长性条件下存在解的充分条件,推广和改进已有的结果,并给出应用实例.

A class of boundary value problem of fractional differential equation with fractional integral conditions is investigated. It involves the Caputo fractional derivative in nonlinear terms and can be reduced to the equivalent integral equation.By using Leray-Schauder nonlinear alternative principle combined with a new inequality of norm form,some sufficient conditions on the exitence of solution for the boundary value problem with some growth conditions are established. Some known results are extended and improved. A example is given to illustrate the application of the result.