MIXED MONOTONE ITERATIVE TECHNIQUE FOR SEMILINEAR IMPULSIVE FRACTIONAL EVOLUTION EQUATIONS

Yongxiang Li; Haide Gou

doi:10.11948/2156-907X.20180202

2019 Volume 9 Issue 4

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Yongxiang Li, Haide Gou. MIXED MONOTONE ITERATIVE TECHNIQUE FOR SEMILINEAR IMPULSIVE FRACTIONAL EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1216-1241. doi: 10.11948/2156-907X.20180202

Citation:

Yongxiang Li, Haide Gou. MIXED MONOTONE ITERATIVE TECHNIQUE FOR SEMILINEAR IMPULSIVE FRACTIONAL EVOLUTION EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1216-1241. doi: 10.11948/2156-907X.20180202

MIXED MONOTONE ITERATIVE TECHNIQUE FOR SEMILINEAR IMPULSIVE FRACTIONAL EVOLUTION EQUATIONS

Yongxiang Li^1,,
Haide Gou^1, ,

1.
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

Author Bio: liyxnwnu@163.com (Y. Li)
Corresponding author: Email address:842204214@qq.com(H. Gou)
Fund Project: The authors were supported by National Natural Science Foundation of China(11661071)

Abstract

Abstract

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.
- Monotone iterative technique /
- coupled L-quasi-upper and lower solutions /
- impulsive fractional evolution equation /
- C₀-semigroup
MSC: 26A33, 34K30, 34K45, 35B10

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References

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