New estimates considering the generalized proportional Hadamard fractional integral operators

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 integr...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 15
Main Authors: Zhou, Shuang-Shuang, Rashid, Saima, Jarad, Fahd, Kalsoom, Humaira, Chu, Yu-Ming
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 09.06.2020
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Difference and Functional Equations
Fractional calculus
Functional Analysis
Generalized proportional Hadamard fractional integral operator
Grüss inequality
Integrals
Mathematics
Mathematics and Statistics
Methods
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Riemann–Liouville fractional integral operator
Topics in Special Functions and q-Special Functions: Theory
26E60
Grüss inequality
Generalized proportional Hadamard fractional integral operator
26D10
Riemann–Liouville fractional integral operator
90C23
Fractional calculus
26D15
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02730-w