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

Existence of Mild Solution for Conformable FractionalNon-instantaneous Imputsive Differential Equationwith Nonlocal Problem

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T qu(t)=Au(t)+f(t,u(t),Gu(t),Su(t)),t∈∪m i=0(s i,t i+1],u(t)=φi(t,u(t)),t∈∪m i=1(t i,s i],u(0)+g(u)=u 0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.

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 T qu(t)=Au(t)+f(t,u(t),Gu(t),Su(t)),t∈∪m i=0(s i,t i+1],u(t)=φi(t,u(t)),t∈∪m i=1(t i,s i],u(0)+g(u)=u 0.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.