一类具有时滞的脉冲分数阶测度微分方程mild解的存在性The Existence of Mild Solutions for a Class of Impulsive Fractional Order Measure Differential Equations with Time Delay
刘文杰
摘要(Abstract)：
在半群非紧的情况下，研究正则函数空间中一类具有时滞的脉冲分数阶测度微分方程mild解的存在性，通过利用算子半群理论、Kuratowski非紧性测度及M?nch不动点定理得出分数阶测度微分方程mild解的存在性．脉冲项的紧性条件、非紧性测度和先验估计的限制条件不再被使用，推广了许多已有的结果，并给出一个具体实例证明了结果的可行性．
关键词(KeyWords)： 正则函数空间;分数阶测度微分方程;非紧性测度;M?nch不动点定理;mild解
基金项目(Foundation): 安徽自然科学基金重点项目（2023AH051433）;; 安徽省教育厅重点项目（2024AH050885）;; 安徽职业技术学院校级项目（2023yjjpkc37）
作者(Author): 刘文杰
DOI: 10.16393/j.cnki.37-1436/z.2025.05.008
参考文献(References)：
- [1]P.C.Das,R.R.Sharma.On Optimal Controls for Measure Delay-differential Equations[J].Siam.J.Control.Optim.,1997,9(01):43-61.
- [2]P.C.Das,R.R.Sharma.Existence and Stability of Measure Differential Equations[J].Czech.M-ath.J.,1972,22(01):145-158.
- [3]B.Brogliato.Nonsmooth Mechanics Models,Dynamics,and Control[M].Berlin,Heidelberg:Springer Berlin Heidelberg,1996.
- [4]徐远通．泛函微分方程与测度微分方程[M]．广州：中山大学出版社，1988.
- [5]M.Federson,J.G.Mesquita,A.Slavik.Measure Functional Differential Equations and Function-al Dynamic Equations Ontime Scales[J].J.Differ.Equations.,2012,252(06):3816-3847.
- [6]H.B.Gu,Y.Sun.Nonlocal Controllability of Fractional Measure Evolution Equation[J].J.Ine-qual.Appl.,2020,2020(01):60-78.
- [7]S.U.Kumar,Agarwal R.P.Agarwal.Existence of Solution for Non-autonomous Semi-linear Measure Driven Equations[J].Differ.Equat.Appl.,2020,12(03):313-322.
- [8]Y.Y.Liu,Y.H.Liu.Controllability of Fractional Measure Evolution Systems with Statedepende-nt Delay and Nonlocal Condition[J].Evol.Equ.Control.The.,2023,12(02):525-541.
- [9]Y.J.Cao,J.T.Sun.Measures of Noncompactness in Spaces of Regulated Functions with Applic-ation to Semilinear Measure Driven Equations[J].Bound.Value.Probl.,2016,2016(38):1-17.
- [10]Y.J.Cao,J.T.Sun.Practical Stability of Nonlinear Measure Differential Equations[J].Nonlin-ear.Anal.Hybri.,2018,30(01):163-170.
- [11]H.D.Gou,Y.X.Li.Existence and Approximate Controllability of Semilinear Measure Driven Systems with Nonlocal Conditions[J].B.Iran.Math.Soc.,2022,48(02):769-789.
- [12]刘文杰．带有非局部条件半线性中立型测度方程的可控性[J]．菏泽学院学报，2021,43(05):13-18.
- [13]H.B.Gou.On the S-asymptoticallyω-periodic Mild Solutions for Multi-term time Fractional Measure Differential Equations[J].Topol.Method.Nonl.An.,2023,62(02):569-590.
- [14]E.Hernndez,R.Marco,R.Hernan.Existence of Solutions for Impulsive Partial Neutral Functi-onal Differential Equations[J].J.Math.Anal.Appl.,2007,331(02):1135-1158.
- [15]V.Rao,H.Sree.Integral Inequalities of Gronwall Type for Distributions[J].J.Math.Anal.A-ppl.,1979,72(02):545-550.
- [16]H.M?ch.Boundary Value Problems for Nonlinear Ordinary Differential Equations of Second Order in Banach Spaces[J].Nonlinear Analysis:Theory Methods Applications,1980,4(05):985-999.