scholarly journals On some new weakly singular Volterra integral inequalities with maxima and their applications

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Yong Yan
Keyword(s):  
Integral Inequalities ◽  
Weakly Singular

scholarly journals Some Nonlinear Gronwall-Bellman-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo ◽  
Min Tang
Keyword(s):  
Integral Equation ◽  
Qualitative Study ◽  
Integral Equations ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Operator ◽  
Power Nonlinearity ◽  
Weakly Singular ◽  
Type Integral ◽  
Fractional Integral Equation

Some Gronwall-Bellman-Gamidov type integral inequalities with power nonlinearity and their weakly singular analogues are established, which can give the explicit bound on solution of a class of nonlinear fractional integral equations. An example is presented to show the application for the qualitative study of solutions of a fractional integral equation with the Riemann-Liouville fractional operator.

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.

scholarly journals Gronwall-Bellman Type Inequalities and Their Applications to Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng
Keyword(s):  
Differential Equations ◽  
Qualitative Analysis ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Integral Inequalities ◽  
Weakly Singular ◽  
Fractional Differential

Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which can be used in the qualitative analysis of the solutions to certain fractional differential equations.

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