一类分数次中立型发展方程mild解的存在性证明

Existence of mild solution for a kind of fractional evolution equation

研究一类新的具有无限延迟的中立型分数次发展方程。利用相空间的性质,以Kuratowski非紧测度为工具,根据不动点定理得到了mild解的存在性定理。最后,给出一个例子来验证结论的有效性。

A kind of fractional neutral evolution equation with infinite delay is investigated.Making use of the properties of phase spaces,we obtain the existence of the mild solution by means of a fixed point theorem in the theory of measure of noncompactness.In addition,an example in form of a partial differential equation is given to illustrate our result.