scholarly journals Some generalizations of delay integral inequalities of Gronwall-Bellman type with power and their applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Haoyue Song ◽  
Fanwei Meng
Keyword(s):  
Integral Equations ◽  
Integral Inequalities ◽  
Qualitative Properties ◽  
Asymptotics Of Solutions ◽  
Explicit Bound ◽  
Differential And Integral Equations

<p style='text-indent:20px;'>Noting the diverse generalizations of the Gronwall-Bellman inequality, this paper investigates some new delay integral inequalities with power, deriving explicit bound on the solution and providing an example. The inequalities given here can act as powerful tools for studying qualitative properties such as existence, uniqueness, boundedness, stability and asymptotics of solutions of differential and integral equations.</p>

scholarly journals A new class of nonlinear Gronwall–Bellman delay integral inequalities with power and its applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bo Fang ◽  
Yujiao Liu ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Qualitative Properties ◽  
New Class ◽  
Convenient Tool ◽  
Qualitative Properties Of Solutions ◽  
Differential And Integral Equations

AbstractIn this paper, we establish some new delay Gronwall–Bellman integral inequalities with power, which can be used as a convenient tool to study the qualitative properties of solutions to differential and integral equations. We also give some examples to illustrate the application of our results to obtain the estimation for the solution of the integral and differential equations.

scholarly journals ON BIVARIATE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

2019 ◽  
pp. 553
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Order ◽  
Time Delays ◽  
Integral Inequalities ◽  
Partial Differential ◽  
Independent Variables ◽  
Fractional Order Differential Equations ◽  
Two Independent Variables ◽  
Differential And Integral Equations

In this paper, we obtain some retarded integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays. The presented inequalities are of new forms compared with the existing ones so far in the literature. In order to illustrate the validity of the theorems we give one application for them for the solution to certain fractional order differential equations.

scholarly journals A note on a certain retarded integral inequality

2005 ◽  
Vol 36 (4) ◽  
pp. 319-325 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Equations ◽  
Integral Inequality ◽  
Present Note ◽  
Explicit Bound ◽  
Differential And Integral Equations

In the present note we establish explicit bound on a certain retarded integral inequality which can be used as a tool in the study of retarded differential and integral equations.

Some New Impulsive Integral Inequalities

2014 ◽  
Vol 536-537 ◽  
pp. 876-879
Author(s):  
Bao Ju Sun
Keyword(s):  
Integral Equations ◽  
Qualitative Theory ◽  
Integral Inequalities ◽  
Differential And Integral Equations

Some new impulsive integral inequalities related to certain integral inequalities are established, which extend the results proved by J. Li in [On some new impulsive integral inequalities, Journal of Inequalities and Applications, Vol. 200. The inequalities given here can be used as basic tools in the qualitative theory of certain impulsive differential and integral equations.

On some Nonlinear Integral Inequalities for Volterra Integral Equations

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
S.D. Kendre ◽  
S.G. Latpate
Keyword(s):  
Integral Equations ◽  
Unknown Function ◽  
Volterra Integral Equations ◽  
Integral Inequalities ◽  
Explicit Bound

Abstract In this paper, we have stated and proved some results on nonlinear integral inequalities and its applications which provide an explicit bound on unknown function and can be used as a tool in the study of certain nonlinear retarded Volterra integral equations.

On generalizations of certain nonlinear integral inequalities and their applications

2018 ◽  
Vol 11 (03) ◽  
pp. 1850032
Author(s):  
S. G. Latpate
Keyword(s):  
Differential Equation ◽  
New York ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Academic Press ◽  
Iterated Integrals ◽  
Retarded Differential Equation ◽  
Differential And Integral Equations

The aim of this paper is to generalize some integral inequalities of Gronwall–Bellman type. We generalize the results presented by Pachpatte in [Inequalities for Differential and Integral Equations (Academic Press, New York, 1998)] and Abdeldaim in [On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation, J. Egypt. Math. Sci. Lett. 23 (2015) 470–475] and also establish some new forms.

scholarly journals On Volterra inequalities and their applications

2004 ◽  
Vol 2004 (3) ◽  
pp. 117-134 ◽  
Author(s):  
Lechosław Hącia
Keyword(s):  
Integral Equations ◽  
Integral Inequalities ◽  
Gronwall Inequality ◽  
Two Dimensional ◽  
Grönwall Inequality ◽  
Differential And Integral Equations

We present certain variants of two-dimensional andn-dimensional Volterra integral inequalities. In particular, generalizations of the Gronwall inequality are obtained. These results are applied in various problems for differential and integral equations.

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