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.
Contents
Introduction
Preliminaries
Fractional integral identities
Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals
Hermite-Hadamard inequalities involving Hadamard fractional integrals
Table of Content:
Chapter 1 Introduction
1.1 Fractional Calculus via Application and Computation
1.2 Motivation of Fractional Hermite-Hadamards Inequality
1.3 Main Contents
Chapter 2 Preliminaries
2.1 Definitions of Special Functions and Fractional Integrals
2.2 Definitions of Convex Functions
2.3 Singular Integrals via Series
2.4 Elementary Inequalities
Chapter 3 Fractional Integral Identities
3.1 Identities involving Riemann-Liouville Fractional Integrals
3.2 Identities involving Hadamard Fractional Integrals
Chapter 4 Hermite-Hadamards inequalities involving Riemann-Liouville
fractional integrals
4.1 Inequalities via Convex Functions
4.2 Inequalities via r-Convex Functions
4.3 Inequalities via s-Convex Functions
4.4 Inequalities via m-Convex Functions
4.5 Inequalities via (s, m)-convex Functions
4.6 Inequalities via Preinvex Convex Functions
4.7 Inequalities via (,m)-geometrically Convex Functions
4.8 Inequalities via geometrical-arithmetically s-Convex Functions
4.9 Inequalities via (,m)-logarithmically Convex Functions
4.10 Inequalities via s-GodunovaLevin functions
4.11 Inequalities via AG(log)-convex Functions
Chapter 5 Hermite-Hadamards inequalities involving Hadamard fractional
integrals
5.1 Inequalities via Convex Functions
5.2 Inequalities via s-e-ondition Functions
5.3 Inequalities via geometric-geometric co-ordinated Convex Function
5.4 Inequalities via Geometric-Geometric-Convex Functions
5.5 Inequalities via Geometric-Arithmetic-Convex Functions
References
Jinrong Wang, Guizhou University, Guiyang, China; Michal Fekan, Comenius University in Bratislava, Slovakia.
