On an Inequality of H. G. Hardy

被引：16

作者：

Iqbal, Sajid ^{[1
]}

Krulic, Kristina ^{[2
]}

Pecaric, Josip ^{[1
,2
]}

机构：

[1] Govt Coll Univ, Abdus Salam Sch Math Sci, Lahore 54600, Pakistan

[2] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2010年

关键词：

Weight Function; Fractional Derivative; Hypergeometric Function; Fractional Integral; Caputo Fractional Derivative;

D O I：

10.1155/2010/264347

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as well as fractional integrals of a function with respect to another function. Finally, we apply our main result to multidimensional settings to obtain new results involving mixed Riemann-Liouville fractional integrals.

引用

页数：23