Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications - Humaira Kalsoom; Zareen A. Khan (Mathematics, 2022)
In this work, we introduce new definitions of left and right-sides generalized conformable <semantics>K</semantics>-fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for <semantics>ϕ</semantics>-preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable <semantics>K</semantics>-fractional integrals regarding <semantics>ϕ</semantics>-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 <semantics>K</semantics>-fractional differential equations to show our new approach.