一致分数阶非瞬时脉冲微分方程非局部问题温和解的存在性

利用算子半群理论、 非紧性测度估计技巧和Darbo’s不动点定理研究一致分数阶非瞬时脉冲微分方程非局部问题温和解的存在性, 在非线性项满足适当增长条件和非紧性测度条件, 非局部项和非瞬时脉冲函数均满足Lipschitz条件下, 得到该问题解的存在性结果, 并举例说明所得结果的有效性.

Existence of Mild Solution for Conformable Fractional Non-instantaneous Imputsive Differential Equation with Nonlocal Problem

By using the theory of operator semigroup, estimation technique of noncompact measure and Darbo’s fixed point theorem, we studied the existence of mild solution for conformable fractional non-instantaneous impulsive differential equation with nonlocal problem. Under the condition that the nonlinear term satisfied the  appropriate growth condition and noncompactness measure condition, and  the nonlocal term and non-instantaneous impulsive function satisfied the  Lipschitz condition, we obtained the existence result of solution of the problem, and gave  an example  to illustrate the effectiveness of the result.