Efficient computations for weighted generalized proportional fractional operators with respect to a monotone function

• Published in: AIMS mathematics Vol. 6; no. 8; pp. 8001 - 8029
• Main Authors: Zhou, Shuang-Shuang, Rashid, Saima, Rauf, Asia, Jarad, Fahd, Hamed, Y. S., Abualnaja, Khadijah M.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: cauchy schwartz inequality; grüss type inequality; weighted chebyshev inequality; weighted generalized proportional fractional integrals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021465

In this paper, we propose a new framework of weighted generalized proportional fractional integral operator with respect to a monotone function Ψ, we develop novel modifications of the aforesaid operator. Moreover, contemplating the so-called operator, we determine several notable weighted Chebyshev and Grüss type inequalities with respect to increasing, positive and monotone functions Ψ by employing traditional and forthright inequalities. Furthermore, we demonstrate the applications of the new operator with numerous integral inequalities by inducing assumptions on ω and Ψ verified the superiority of the suggested scheme in terms of efficiency. Additionally, our consequences have a potential association with the previous results. The computations of the proposed scheme show that the approach is straightforward to apply and computationally very user-friendly and accurate.