Nonlinear Gronwall–Bellman Type Inequalities and Their Applications

Weimin Wang, Yuqiang Feng and Yuanyuan Wang
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Weimin Wang: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
Yuqiang Feng: Hubei Province Key Laboratory of Systems Science in Metallurgical Process , Wuhan 430065, China
Yuanyuan Wang: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China

Mathematics, 2017, vol. 5, issue 2, 1-11

Abstract: In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.

Keywords: nonlinear Gronwall–Bellman inequalities; differential equation; integral equation; Hyers–Ulam stability; boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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