Results 1 to 10 of about 606,903 (214)
Note on fractional difference Gronwall inequalities
Electronic Journal of Qualitative Theory of Differential Equations, 2014 This note is a reaction on a bunch of fractional inequalities that appeared in the last few years, and that are all based on what claims to be a fractional discrete Gronwall inequality.
Michal Fečkan, Michal Pospíšil
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New Results for Generalized Gronwall Inequalities and Their Applications
Abstract and Applied Analysis, 2014 In succession to our earlier work, we further provide some new generalized Gronwall inequalities and apply these inequalities to the study of qualitative estimations of solutions to certain fractional differential equations.
Shi-you Lin
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On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications [PDF]
Journal of Inequalities and Applications, 2005 Some new Gronwall-Ou-Iang type integral inequalities in two independent variables are established. These integral inequalities can be applied as tools to the study of certain class of integral and differential equations.
Ma Qing-Hua, Cheung Wing-Sum
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Journal of Inequalities and Applications, 2022 The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales ...
Ahmed A. El-Deeb, Dumitru Baleanu
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Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications [PDF]
Journal of Inequalities and Applications, 2017 The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities.
Zizun Li, Wu-Sheng Wang
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Some New Generalized Retarded Gronwall-Like Inequalities and Their Applications in Nonlinear Systems
Journal of Control Science and Engineering, 2016 The Gronwall inequalities are of significance in mathematics and engineering. This paper generalizes the Gronwall-like inequalities from different perspectives.
Haiyong Qin, Xin Zuo, Jianwei Liu
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Nonlinear Gronwall–Bellman Type Inequalities and Their Applications
Mathematics, 2017 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 ...
Weimin Wang, Yuqiang Feng, Yuanyuan Wang
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Discrete Grönwall inequalities for demimartingales [PDF]
Communications in Statistics - Theory and Methods, 2023 . The aim of this work is to obtain discrete versions of stochastic Grönwall inequalities involving demimartingale sequences. The results generalize the respective theorems for martingales provided by Kruse and Scheutzow (2018) and Hendy et al. (2022).
M. Hadjikyriakou, B. Prakasa Rao
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AIMS Mathematics, 2022 In this paper, we obtain a new generalized coupled Gronwall inequality through the Caputo fractional integral with respect to another function $ \psi $. Based on this result, we prove the existence and uniqueness of solutions for nonlinear delay coupled $
Ding-De Jiang, C. Bai
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AIMS Mathematics, 2022 In this paper, a Gronwall inequality involving $ \psi $-fractional integral operator is obtained as a generalization of [23]. An example is listed to show the applications.
Qi Wang, Shumin Zhu
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