CAJ | 학술논문

研究了一类具有Riemann-Liouville分数阶积分条件的新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，应用Leray-Schauder不动点定理结合一个范数形式的新不等式，获得了解的存在性充分条件，推广和改进了已有的结果，并给出了应用实例。
연구료일류구유Riemann-Liouville분수계적분조건적신분수계미분방정변치문제，기비선성항포함Caputo형분수계도수。장해문제전화위등개적적분방정，응용Leray-Schauder불동점정리결합일개범수형식적신불등식，획득료해적존재성충분조건，추엄화개진료이유적결과，병급출료응용실례。
A class of boundary value problem of fractional differential equation with Riemann-Liouville fractional integral conditions is investigated, which involves the Caputo fractional derivative in nonlinear terms and can be reduced to the equivalent integral equation. By using Leray-Schauder fixed point theory combined with a new inequality of norm form, some sufficient conditions on the exitence of solution for boundary value problem are established. Some known results are extended and improved. An example is given to illustrate the application of the result.