研究了Caputo分数阶微分方程初值问题解的存在性,运用Ascoli-Arzela’s定理证明了初值问题局部解的存在性,并对极值解的存在性加以考虑,作为比较定理的应用,最后对初值问题全局解的存在性进行了讨论.
In this paper, the existence results of solutions for fractional initial value problem involving Caputo differential operators is discussed. As application of Ascoli-Arzela' s theorem, we prove the local existence result and consider the existence of extremal solutions. Using the comparison result, we discuss a global existence result in the end.