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Mathematics 2017, 5(2), 31; doi:10.3390/math5020031

Nonlinear Gronwall–Bellman Type Inequalities and Their Applications

1
School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
2
Hubei Province Key Laboratory of Systems Science in Metallurgical Process , Wuhan 430065, China
*
Author to whom correspondence should be addressed.
Received: 2 February 2017 / Revised: 6 May 2017 / Accepted: 23 May 2017 / Published: 31 May 2017
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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. View Full-Text
Keywords: nonlinear Gronwall–Bellman inequalities; differential equation; integral equation; Hyers–Ulam stability; boundedness nonlinear Gronwall–Bellman inequalities; differential equation; integral equation; Hyers–Ulam stability; boundedness
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, W.; Feng, Y.; Wang, Y. Nonlinear Gronwall–Bellman Type Inequalities and Their Applications. Mathematics 2017, 5, 31.

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