Di̇fferent types of integral inequalities including Katugampola fractional integral operators

This thesis consists of four chapters. In the first section, which is the introduction section; the historical development of the concept of inequality, which is one of the important and major subjects of mathematics, and the historical development of the convex functions and the historical development of fractional derivative-fractional integral. In the second part; In our thesis, some functions definitions, convex function classes and place of reference are given. In the third chapter, some theorem studies including Hermit-Hadamart type inequalities and katugampola fractional inequalities, s-convex class are given. In the last section, the findings examined in the section of the study, based on the theorems of the Katugampola fractional integral operator with different types of inequalities have been obtained.