【摘要】 该文讨论了具有分段Caputo导数和周期脉冲的分数阶发展方程,建立了具有周期脉冲的相关线性发展方程周期mild解的存在性和唯一性.借助线性脉冲周期问题解算子的表达式,利用算子半群理论和不动点定理,证明了半线性脉冲周期问题周期mild解的一些新的存在性结果.更多还原

【Abstract】 This paper discusses the fractional evolution equations with piecewise Caputo derivative and periodic impulses.The existence and uniqueness of periodic mild solutions for the associated linear evolution equation with periodic impulses is established.With the aid of the expression of the solution operator for the linear impulsive periodic problem,some new existence results of periodic mild solutions for semilinear impulsive periodic problems are showed by means of the operator semigroup theory and fixed point theorems.更多还原