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

Humaira Kalsoom and Zareen A. Khan
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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

Mathematics, 2022, vol. 10, issue 3, 1-20

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.

Keywords: Hermite-Hadamard; ? -preinvex function; generalized conformable K -fractional derivative; generalized conformable K -fractional integral; Hölder’s inequality; power mean inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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