SINGULAR INTEGRODIFFERENTIAL INEQUALITIES AND APPLICATION TO FRACTIONAL DIFFERENTIAL PROBLEMS

被引：0

作者：

Lakhal, Fahim ^{[1
]}

Tatar, Nasser-Eddine ^{[2
]}

机构：

[1] Univ 08 Mai 45, Dept Math, Guelma 24000, Algeria

[2] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2011年 / 14卷 / 04期

关键词：

Integrodifferential inequalities; Riemann; Liouville fractional integral; singular kernel; weighted Cauchy-type fractional problem; INTEGRAL-INEQUALITIES; EQUATIONS; BOUNDS; BIHARI;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we are concerned with an integrodifferential problem which arises for instance when we study a Cauchy- type fractional differential equation. This problem involves a convolution of a kernel with a nonlinear function of the solution together with its derivatives up to order two. For ordinary (third order) differential equations the kernel is regular while in our case it is singular and nonintegrable. Combining a desingularization technique due to the second author with some other estimations, we find bounds for solutions of the problem with different nonlinearities. Our results are illustrated by an application to fractional differential equations.

引用

页码：867 / 880

页数：14

共 21 条

[1]

[Anonymous], 1993, DISSERTATIONES MATH

[2]

[Anonymous], 2006, Journal of the Electrochemical Society

[3]

Bainov D., 1992, Integral inequalities and applications, V57

[4] GENERALIZATION OF A LEMMA OF BIHARI AND APPLICATIONS TO POINTWISE ESTIMATES FOR INTEGRAL EQUATIONS [J].