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

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.

New Hermite–Hadamard Integral Inequalities for Geometrically Convex Functions via Generalized Weighted Fractional Operator

“…This finding piqued the interest of numerous researchers, who began investigating the subject further. For further information, as well as recent results and newly discovered properties pertaining to this operator, please see [7][8][9][10][11][12][13][14][15][16].…”