Generalized weakly singular integral inequalities with applications to fractional differential equations with respect to another function

2020 ◽  
Vol 50 (6) ◽  
pp. 2001-2010
Author(s):  
Salah Boulares ◽  
Abdellatif Ben Makhlouf ◽  
Hassane Khellaf
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Integral Inequalities ◽  
Weakly Singular ◽  
Fractional Differential

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 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.

Sign in / Sign up

Export Citation Format

Share Document