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.

scholarly journals A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanhua Lin ◽  
Shanhe Wu ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Integral Inequality ◽  
Analysis Techniques ◽  
Weakly Singular ◽  
Type Integral ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Equations With Delay

We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.

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 Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Phollakrit Thiramanus ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Inequalities ◽  
Weakly Singular ◽  
Type Integral ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

Some new weakly singular Henry-Gronwall type integral inequalities with “maxima” are established in this paper. Applications to Caputo fractional differential equations with “maxima” are also presented.

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