Three Types Of Fractional Integral Inequalities For Generalized Convex Functions

Based on three types of fractional integrals,we study some fractional integral inequalities for several generalized convex functions.Some inequalities established in the paper are the generalizations of existing results in the literature.This paper is divided into the following five chapters:In Chapter 1,we review the concepts of fractional integrals and expound the development of three types of fractional integral inequalities.In Chapter 2,based on Hadamard k-fractional integrals,we study the Fejér-type inequalities for GA-s-convex functions.Firstly,we construct a new k-fractional integral identity.Then based on this identity,we establish some new k-fractional integral inequalities for GA-s-convex functions.Finally,using the GA-s-convexity,we obtain some integral inequalities of product type.In Chapter 3,we construct a Riemann-Liouville k-fractional integral identity,and establish some Simpson-type k-fractional integral inequalities.In Chapter 4,by using Katugampola fractional integral,we construct a parameteried Ostrowski-type fractional integral identity.Based on this integral identity,we establish some integral inequalities for p-convex functions.Taking different values for the parameter,we obtain different types of integral inequalities.In Chapter 5,we summarize the main contents of this paper and provide some ideas for further study involving fractional integral inequality.