Banach空间中分数阶微分方程初值问题解的性质

The properties of solutions for initial value problems of fractional differential equations in Banach space

讨论了Banach空间中的分数阶微分方程解的性质,利用Schauder不动点定理及Gronwall不等式证明了初值问题解的存在唯一性.当右端函数f(t,u)关于u线性增长时,得到了解的整体存在性.进一步讨论了分数阶方程的解对初值和阶数的连续相依性.

This paper mainly investigate the properties of solutions for fractional differential equations in Banach space.By Schauder fixed-point theorem and Gronwall inequality,the existence and uniqueness of solutions on initial value problems are proved.When the function on right side of equality is growing linearly,the global existing interval of the solutions is in [0,＋∞）.Furthermore,we study the dependence of solutions for fractional differential equations on the continuity of initial values and orders.