Newton-type inequalities for fractional integrals

This thesis is about Newtonian inequalities for fractional integrals. The first part of this study, which consists of five chapters, is an introduction, and the second part includes some basic definitions and theorems that need to be known for the thesis. Then, after giving necessary definitions and theorems about fractional integrals and generalized fractional integrals, Newtonian inequalities are mentioned. The third part is the important part for the thesis study. Newtonian inequalities for single-variable differentiable convex functions were studied in two parts. In our fourth chapter, two-variable differentiable convex functions are included, and they are studied in two parts to ensure diversity. While carrying out these studies, the relations of the obtained inequalities with functions with limited variation were also examined. In the last section, some conclusions and suggestions for further studies are given.