Inequalities by means of generalized proportional fractional integral operators with respect to another function

Abstract

In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ. The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Y and the proportionality index ζ. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems. © 2019 by the authors.