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Hermite-Hadamard-Fejér Type Inequalities with Generalized K -Fractional Conformable Integrals and Their Applications

Author

Listed:
  • Humaira Kalsoom

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

  • Zareen A. Khan

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

In this work, we introduce new definitions of left and right-sides generalized conformable K -fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for ϕ -preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable K -fractional integrals regarding ϕ -preinvex functions. Finally, we also present some applications of the generalized definitions for higher moments of continuous random variables, special means, and solutions of the homogeneous linear Cauchy-Euler and homogeneous linear K -fractional differential equations to show our new approach.

Suggested Citation

  • Humaira Kalsoom & Zareen A. Khan, 2022. "Hermite-Hadamard-Fejér Type Inequalities with Generalized K -Fractional Conformable Integrals and Their Applications," Mathematics, MDPI, vol. 10(3), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:483-:d:740749
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    References listed on IDEAS

    as
    1. Sikander Mehmood & Fiza Zafar & Nusrat Yasmin, 2019. "Hermite-Hadamard-Fejér Type Inequalities for Preinvex Functions Using Fractional Integrals," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
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