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Volume 9, Number 4, 2019, Pages 1216-1241                                                                DOI:10.11948/2156-907X.20180202
Mixed monotone iterative technique for semilinear impulsive fractional evolution equations
Yongxiang Li,Haide Gou
Keywords:Monotone iterative technique, coupled L-quasi-upper and lower solutions, impulsive fractional evolution equation, C_0-semigroup.
      In this paper, we deals with the existence of mild $L$-quasi-solutions to the boundary value problem for a class of semilinear impulsive fractional evolution equations in an ordered Banach space $E$. Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive fractional evolution equations has been established. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. As some application that illustrate our results, An example is also given.
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