分数阶共振向量边值问题解的存在性

Existence of Solutions for Fractional Order Vector Boundary Value Problems at R esonance

研究了一类带有系数矩阵的分数阶共振边值问题.首先,定义2个合适的Banach空间;然后,在Banach空间中构造恰当的算子并使用仿伪逆矩阵的性质及Mawhin的重合度理论,得到了其解的存在性;最后,给出一个例子来验证主要结果.

This paper studies the fractional boundary value problems(BVPs)with a matrix of coefficients at resonance.First,we construct two suitable Banach spaces.Then,the existence of fractional vector BVPs is obtained by defining an appropriate operator in Banach space using the properties of pseudoinverse matrices and Mawhin's coincidence degree theory.Finally,we give examples to illustrate the main results.