This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus.

ContentsIntroductionPreliminariesFractional integral identitiesHermite-Hadamard inequalities involving Riemann-Liouville fractional integralsHermite-Hadamard inequalities involving Hadamard fractional integrals

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

Table of Content:Chapter 1 Introduction1.1 Fractional Calculus via Application and Computation1.2 Motivation of Fractional Hermite-Hadamards 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-Hadamards 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 (,m)-geometrically Convex Functions4.8 Inequalities via geometrical-arithmetically s-Convex Functions4.9 Inequalities via (,m)-logarithmically Convex Functions4.10 Inequalities via s-GodunovaLevin functions4.11 Inequalities via AG(log)-convex FunctionsChapter 5 Hermite-Hadamards 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