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Journal of Advances in Applied Mathematics
JAAM > Volume 5, Number 2, April 2020

Existence and Uniqueness of Solutions of Integer Order Differential Equations with Non-Instantaneous Impulses

Download PDF  (346.2 KB)PP. 71-77,  Pub. Date:March 31, 2020
DOI: 10.22606/jaam.2020.52003

Author(s)
WenJing Zheng
Affiliation(s)
College of Science, University of Shanghai for Science and Technology, Shanghai, P. R. China
Abstract
We study the existence and uniqueness of solutions for a class of integer order differential equations with non-instantaneous. Firstly, the differential boundary value problem is transformed into an equivalent integral equation problem, and then the existence results of the solution and the sufficient conditions for the existence of the solutions are obtained by using Schauder fixed point theory. The uniqueness theorem of the solution is established by using contraction mapping principle.
Keywords
non-instantaneous impulsive, Caputo derivative, contraction mapping principle, Schauder fixed point theorem
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