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

• Published in: AIMS mathematics Vol. 6; no. 9; pp. 9154 - 9176
• Main Authors: Zhou, Shuang-Shuang, Rashid, Saima, Set, Erhan, Ahmad, Abdulaziz Garba, Hamed, Y. S.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: cauchy schwartz inequality; pólya-szegötype inequality; weighted chebyshev inequality; weighted generalized proportional hadamard fractional integrals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021532

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.