Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function

By Saima Rashid, Fahd Jarad, Muhammad Aslam Noor, Humaira Kalsoom, Y. Chu. 2019

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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 Ψ and the proportionality index ς . 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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6d13eb3d208c31919360bcc0f300302b15b09338

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

On more general forms of proportional fractional operators (2019, background): “[33] Let σ ∈ (0, 1], Re(ω) > 0 and Re(η) > 0.”