New estimates considering the generalized proportional Hadamard fractional integral operators

Advances in Difference Equations

article

Zhou, Shuang-Shuang¹  Rashid, Saima²  Jarad, Fahd³  Kalsoom, Humaira⁴  Chu, Yu-Ming⁵ 

[1] School of Science, Hunan City University;Department of mathematics, Government University;Department of Mathematics, Çankaya University;School of Mathematical Sciences, Zhejiang University;Department of Mathematics, Huzhou University;Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology

关键词: Grüss inequality;    Fractional calculus;    Generalized proportional Hadamard fractional integral operator;    Riemann–Liouville fractional integral operator;   

DOI  :  10.1186/s13662-020-02730-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators.

【 授权许可】

CC BY