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Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye


In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

Digital Object Identifier (DOI):

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