Extensions of Gronwall-Bellman type integral inequalities with two independent variables-Reference-Cited by-同舟云学术

Extensions of Gronwall-Bellman type integral inequalities with two independent variables

Published:2022-01-01 Issue:1 Volume:20 Page:431-446
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Xie Yihuai¹,Li Yueyang²³,Liu Zhenhai²

Affiliation:

1. College of Art and Design, Hunan First Normal University , Changsha , 410205, Hunan Province , P. R. China

2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities , Nanning , 530006, Guangxi Province , P. R. China

3. Department of Mathematics, Guangxi Normal University for Nationalities , Chong Zuo , 532200, Guangxi Province , P. R. China

Abstract

Abstract In this paper, we establish several kinds of integral inequalities in two independent variables, which improve well-known versions of Gronwall-Bellman inequalities and extend them to fractional integral form. By using these inequalities, we can provide explicit bounds on unknown functions. The integral inequalities play an important role in the qualitative theory of differential and integral equations and partial differential equations.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0029/pdf

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