Integral inequalities via raina fractional integral operator for exponential and h-convex functions

In this thesis, the Raina fractional integral operators, which are defined in the literature, have been studied, and new integral inequalities have been obtained for the classes of $h$-convex and exponential-convex functions. In the first chapter, convex functions, the history, importance and usage areas of the theory of inequality and fractional calculus are briefly mentioned and information about the studies in the literature is given. In the second chapter, the theoretical foundations, the basic definitions and concepts for convex functions are presented, followed by a discussion on the relationships between different convex function classes. The third chapter provides the basic definitions and concepts related to Raina fractional integral operators, various integral inequalities previously obtained for these fractional integral operators, and the proof methods of these inequalities. Additionally, a detailed literature review on $h$-convex and exponential-convex function classes is presented in this chapter. In the fourth chapter, new integral inequalities for the $h$-convex and exponential-convex function classes are obtained.