Hadamard-type fractional differential equations for the system of integral inequalities on time scales

ABSTRACT

This paper investigates some system of integral inequalities of one independent variable on time scales. The conclusion can be obtained by using Hadamard-type fractional differential equations and Greene's method which bring together and expand some integral inequalities on time scales. The established inequalities give explicit bounds on unknown functions which can be utilized as a key in examining the properties of certain classes of partial dynamic equations and difference equations on time scales. As an application, a system of fractional differential equations is considered to explain the value of our results.     

时标上的推广的Pachpatte型不等式及其在边值问题中的应用

该文利用单调化技巧研究了时标上的推广的Pachpatte型不等式, 该不等式右端有一个非常数项和三个包含未知函数与没有假设单调性的非线性函数的复合函数的积分项, 不等式左端是未知函数与非线性函数的复合函数. 所得不等式不仅把Pachpatte型不等式的离散形式和连续形式统一起来, 而且推广了已有的时标上的相应不等式. 最后, 用得到的结果研究时标上边值问题解的估计.     

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Half-linear Volterra-Fredholm type integral inequalities on time scales and their applications

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Some Generalized Gronwall-like Retarded Inequalities in two independent variables on Time Scales

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On weighted Iyengar type inequalities on time scales

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Gronwall-Bellman type nonlinear delay integral inequalities on time scales

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Generalized Hardy,Copson, Leindler and Bennett inequalities on time scales

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Weighted Hardy-Type Inequalities on Time Scales with Applications

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On weighted Ostrowski type,Trapezoid type,Grüss type and Ostrowski–Grüss like inequalities on time scales

In this paper, we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski-type, Trapezoid-type, Grüss-type and Ostrowski–Grüss-like inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.     

Some nonlinear dynamic inequalities on time scales

The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736–751).     

Halanay type inequalities on time scales with applications

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Permanence of an N-species cooperation system with time delays and feedback controls on time scales

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Explicit bounds on some new nonlinear integral inequalities with delay

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Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay.     

一类积分不等式的推广

对一些基本的积分不等式进行了推广，给出了含有n个无关变元的更广泛的非线性积分不等式．利用所得的不等式讨论了某些非线性积分方程解的有界性．