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On more general inequalities for weighted generalized proportional Hadamard fractional integral operator with applications

Authors :
Shuang-Shuang Zhou
Saima Rashid
Erhan Set
Abdulaziz Garba Ahmad
Y. S. Hamed
Source :
AIMS Mathematics, Vol 6, Iss 8, Pp 9154-9176 (2021)
Publication Year :
2021
Publisher :
AIMS Press, 2021.

Abstract

Fractional calculus has been the target of the work of many mathematicians for more than a century. Some of these investigations are of inequalities and fractional integral operators. In this article, a novel fractional operator which is known as weighted generalized proportional Hadamard fractional operator with unknown attribute weight is proposed. First, a fractional formulation is constructed, which covers a subjective list of operators. With the aid of the above mentioned operators, numerous notable versions of Pólya-Szegö, Chebyshev and certain related variants are established. Meanwhile, new outcomes are introduced and new theorems are exhibited. Taking into account the novel generalizations, our consequences have a potential association with the previous results. Furthermore, we demonstrate the applications of new operator with numerous integral inequalities by inducing assumptions on weight function ϖ and proportionality index φ. It is hoped that this research demonstrates that the suggested technique is efficient, computationally, very user-friendly and accurate.

Details

Language :
English
ISSN :
24736988
Volume :
6
Issue :
8
Database :
Directory of Open Access Journals
Journal :
AIMS Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.7adcf0b64b7d484ea2e3a2b6a720a730
Document Type :
article
Full Text :
https://doi.org/10.3934/math.2021532?viewType=HTML