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

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 3; p. 483
Main Authors Kalsoom, Humaira, Khan, Zareen A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2022
Subjects
Applied mathematics
Calculus
Continuity (mathematics)
Differential equations
Fractional calculus
generalized conformable K-fractional derivative
generalized conformable K-fractional integral
Hermite-Hadamard
Hölder’s inequality
Identities
Integrals
Mathematics
power mean inequality
Random variables
ϕ-preinvex function
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10030483