Results 191 to 200 of about 37,785 (206)

Some new generalized Gronwall–Bellman type discrete fractional inequalities

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalization of a retarded Gronwall-like inequality and its applications

Applied Mathematics and Computation, 2005
In the present paper, an explicit bound on the generalization of a certain retarded integral inequality is given. Some applications are given to illustrate the usefulness of the result.
Agarwal, Ravi P., Deng, Shengfu, Zhang, Weinian   +2 more
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A generalized h-fractional Gronwall's inequality and its applications for nonlinear h-fractional difference systems with ‘maxima’

Journal of difference equations and applications (Print), 2019
This paper gives a generalized h-fractional Gronwall's inequality. Applying this result, we prove the uniqueness and give bounds on solutions for a nonlinear h-fractional difference system with ‘maxima’.
Xianghu Liu, A. Peterson, Baoguo Jia, L. Erbe   +3 more
semanticscholar   +1 more source

Generalizations of Gronwall’s type integral inequalities with singular kernel

AIP Conference Proceedings, 2015
In this paper, the generalization of Gronwall’s type integral inequalities with singular kernel are established. In applications, theorems on stability estimates for the solution of the nonlinear integral equation and the integral-differential equation of the parabolic type are presented.
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Generalization of Lemma Gronwall–Bellman on Retarded Integral Inequality

2012
On the basis of the integral inequalities in [9], this paper establish several general form Gronwall–Bellman nonlinear retarded integral inequalities, which contain multi-different power terms of unknown function inside integral sign. Using integral and differential skills, we obtain some new results which provide explicit bounds on unknown functions ...
Wu-Sheng Wang, Zhengfang Mo, Zongyi Hou
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A general form of Gronwall inequality with Stieltjes integrals

Journal of Mathematical Analysis and Applications
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Claudio A. Gallegos, Ignacio Márquez Albés, Antonín Slavík   +2 more
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Generalized Gronwall–Bellman-type delay dynamic inequalities on time scales and their applications

Applied Mathematics and Computation, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng, Qinghua, Zheng, Bin
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Gronwall’s inequality and stability analysis of nonlinear fractional difference equations

Journal of Nonlinear, Complex and Data Science
This paper investigates the existence and uniqueness of solutions for nonlinear fractional difference equations of the Hilfer type using Brouwer’s and Banach’s fixed-point theorems.
Anshul Sharma, S. N. Mishra, Anurag Shukla   +2 more
semanticscholar   +1 more source

Nonlinear discrete generalizations of Gronwall's inequality

1991
Suppose that \(L\), \(M: \mathbb{N}_ 0\times \mathbb{R}^ +\to \mathbb{R}^ +\) satisfy \(0\leq L(n,x)- L(n,y)\leq M(n,y) (x- y)\) for \(n\in \mathbb{N}_ 0\) and \(x\geq y\geq 0\). Let \(x\), \(A\), \(B: \mathbb{N}_ 0\to \mathbb{R}^ +\) be such that \(x(0)\leq A(0)\) and \[ x(n)\leq A(n)+ B(n) \sum^{n-1}_{k= 0} L(k,x(k)),\quad n\in\mathbb{N}. \] Then for
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General fractional interval-valued differential equations and Gronwall inequalities

Soft Computing, 2023
Qin Fan, Lan-Lan Huang, Guo-Cheng Wu
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