分数阶微分不等式及其在分数阶奇摄动初值问题中的应用（英文）

Fractional Differential Inequality and its Application of Fractional Singularly Perturbed Initial Value Problems

利用分数阶微分方程与微分不等式之间的关系,得到了分数阶微分不等式的相关理论.基于此理论研究了分数阶微分方程的奇摄动初值问题,证明了其解的存在性.同时通过恰当不等式的解,估计了方程的精确解,进而得到分数阶奇摄动初值问题解的存在性及其渐进行为的一般结论..

By analyzing the relation of solutions between fractional differential inequalities and fractional differential equations, the theory of fractional differential inequalities is obtained. And based on the theory, the singularly perturbed initial value problem of fractional differential equations is studied and the existence of solutions is proved. In terms of the solutions of an appropriate inequalities,the exact solution is estimated and then the general results about the initial value problem is established.