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 Relevance of Factorization Method to Differential and Integral Equations Associated with Hybrid Class of Polynomials

2021 ◽  
Vol 6 (1) ◽  
pp. 5
Author(s):  
Naeem Ahmad ◽  
Raziya Sabri ◽  
Mohammad Faisal Khan ◽  
Mohammad Shadab ◽  
Anju Gupta
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Differential Equations ◽  
Integral Equations ◽  
Recurrence Relations ◽  
Factorization Method ◽  
New Class ◽  
Hybrid Class ◽  
Sheffer Polynomials ◽  
Differential And Integral Equations

This article has a motive to derive a new class of differential equations and associated integral equations for some hybrid families of Laguerre–Gould–Hopper-based Sheffer polynomials. We derive recurrence relations, differential equation, integro-differential equation, and integral equation for the Laguerre–Gould–Hopper-based Sheffer polynomials by using the factorization method.

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>

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Qualitative Properties of Solutions of Second-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1520 ◽  
Author(s):  
Omar Bazighifan ◽  
Marianna Ruggieri ◽  
Shyam Sundar Santra ◽  
Andrea Scapellato
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Qualitative Properties ◽  
Neutral Differential Equations ◽  
Functional Differential ◽  
Qualitative Properties Of Solutions

In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results.

scholarly journals On the Mohand Transform and Ordinary Differential Equations with Variable Coefficients

2020 ◽  
Vol 35 (1) ◽  
pp. 01-06
Author(s):  
Mohamed E. Attaweel ◽  
Haneen Almassry
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Integral Transform ◽  
Variable Coefficients ◽  
Sumudu Transforms ◽  
Differential And Integral Equations

The Mohand transform is a new integral transform introduced by Mohand M. Abdelrahim Mahgoub to facilitate the solution of differential and integral equations. In this article, a new integral transform, namely Mohand transform was applied to solve ordinary differential equations with variable coefficients by using the modified version of Laplace and Sumudu transforms.

scholarly journals Some new weakly singular integral inequalities with discontinuous functions for two variables and their applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yaoyao Luo ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Qualitative Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Integral Inequalities ◽  
Independent Variables ◽  
Discontinuous Functions ◽  
Weakly Singular ◽  
Two Independent Variables

Abstract This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative analysis of various problems for integral equations and differential equations. Some examples are also given to illustrate the application of the conclusion.

Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations

2018 ◽  
Vol 68 (1) ◽  
pp. 77-88
Author(s):  
Marcin Borkowski ◽  
Daria Bugajewska
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Integral Equations ◽  
Bounded Variation ◽  
Volterra Integral Equation ◽  
Functions Of Bounded Variation ◽  
Hammerstein Integral Equation ◽  
Linear Differential ◽  
Unbounded Intervals ◽  
Differential And Integral Equations

Abstract In this paper we are going to apply the Henstock-Kurzweil integrals defined on an unbounded intervals to differential and integral equations defined on such intervals. To deal with linear differential equations we examine convolution involving functions integrable in Henstock-Kurzweil sense. In the case of nonlinear Hammerstein integral equation as well as Volterra integral equation we look for solutions in the space of functions of bounded variation in the sense of Jordan.

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