Fractional Hermite-Hadamard Inequalities

Jinrong Wang, Guizhou University, Guiyang, China; Michal Fečkan, Comenius University in Bratislava, Slovakia.

• Table of Content:Chapter 1 Introduction1.1 Fractional Calculus via Application and Computation1.2 Motivation of Fractional Hermite-Hadamard’s Inequality1.3 Main ContentsChapter 2 Preliminaries2.1 Definitions of Special Functions and Fractional Integrals2.2 Definitions of Convex Functions2.3 Singular Integrals via Series2.4 Elementary InequalitiesChapter 3 Fractional Integral Identities3.1 Identities involving Riemann-Liouville Fractional Integrals3.2 Identities involving Hadamard Fractional IntegralsChapter 4 Hermite-Hadamard’s inequalities involving Riemann-Liouville fractional integrals4.1 Inequalities via Convex Functions4.2 Inequalities via r-Convex Functions4.3 Inequalities via s-Convex Functions4.4 Inequalities via m-Convex Functions4.5 Inequalities via (s, m)-convex Functions4.6 Inequalities via Preinvex Convex Functions4.7 Inequalities via (β,m)-geometrically Convex Functions4.8 Inequalities via geometrical-arithmetically s-Convex Functions4.9 Inequalities via (α,m)-logarithmically Convex Functions4.10 Inequalities via s-GodunovaLevin functions4.11 Inequalities via AG(log)-convex FunctionsChapter 5 Hermite-Hadamard’s inequalities involving Hadamard fractional integrals5.1 Inequalities via Convex Functions5.2 Inequalities via s-e-ondition Functions5.3 Inequalities via geometric-geometric co-ordinated Convex Function5.4 Inequalities via Geometric-Geometric-Convex Functions5.5 Inequalities via Geometric-Arithmetic-Convex FunctionsReferences