Yejuan Wang, Fengshuang Gao, Peter Kloeden
Abstract:
A general theorem on the local and global existence of solutions is
established for an impulsive fractional delay differential equation
with Caputo fractional substantial derivative in a separable Hilbert
space under the assumption that the nonlinear term is weakly continuous.
The uniqueness of solutions is also considered under an additional
Lipschitz assumption.
Submitted October 5, 2016. Published November 14, 2017.
Math Subject Classifications: 34K45, 34G20.
Key Words: Impulsive fractional delay differential equation; global solution;
Caputo fractional time derivative.
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Yejuan Wang School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou 730000, China email: wangyj@lzu.edu.cn |
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Fengshuang Gao School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou 730000, China email: gfs16@mails.tsinghua.edu.cn |
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Peter Kloeden School of Mathematics and Statistics Huazhong University of Science & Technology Wuhan 430074, China email: kloeden@math.uni-frankfurt.de |
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