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

Author

Listed:
  • Saima Rashid

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Fahd Jarad

    (Department of Mathematics, Cankaya University, 06790 Ankara, Turkey)

  • Muhammad Aslam Noor

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Humaira Kalsoom

    (School of Mathematical Sciences, Zhejiang Universoty, Hangzhou 310027, China)

  • Yu-Ming Chu

    (Department of Mathematics, Huzhou University, Huzhou 313000, China)

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 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.

Suggested Citation

  • Saima Rashid & Fahd Jarad & Muhammad Aslam Noor & Humaira Kalsoom & Yu-Ming Chu, 2019. "Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function," Mathematics, MDPI, vol. 7(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1225-:d:296714
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    References listed on IDEAS

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    1. Jessada Tariboon & Sotiris K. Ntouyas & Weerawat Sudsutad, 2014. "Some New Riemann-Liouville Fractional Integral Inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-6, March.
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