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 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.

Several Estimations of a Class of Integral Inequality in Engineering

2014 ◽  
Vol 962-965 ◽  
pp. 2748-2751
Author(s):  
Wu Sheng Wang ◽  
Ji Ting Huang
Keyword(s):  
Singular Integral ◽  
Integral Inequality ◽  
Analysis Techniques ◽  
Amplification Method ◽  
Weakly Singular ◽  
Change Of Variable ◽  
Explicit Bounds

In this paper, we discuss a class of new nonlinear weakly singular integral inequality. Under different assumptions, the inequality is solved by analysis techniques, such as: change of variable, amplification method, and three explicit bounds for the unknown functions are given clearly.

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.

scholarly journals New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Quantitative Analysis ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Continuous Dependence ◽  
Initial Value ◽  
Liouville Fractional Derivative ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Differential And Integral Equations

Some new Gronwall-Bellman type inequalities are presented in this paper. Based on these inequalities, new explicit bounds for the related unknown functions are derived. The inequalities established can also be used as a handy tool in the research of qualitative as well as quantitative analysis for solutions to some fractional differential equations defined in the sense of the modified Riemann-Liouville fractional derivative. For illustrating the validity of the results established, we present some applications for them, in which the boundedness, uniqueness, and continuous dependence on the initial value for the solutions to some certain fractional differential and integral equations are investigated.

scholarly journals Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yongqing Wang
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Integral Conditions ◽  
Interesting Point ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Conjugate Type

In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.

Sign in / Sign up

Export Citation Format

Share Document