Examination of some integral inequalities with the help of generalized fractional digit integral operators.

In the first part of this thesis, the concept of convexity, the history of fractional analysis and the working areas of the concept of inequalities are given. In the second chapter, basic definitions and properties of convex functions and some different types of convex function classes are given. In the third chapter, some basic inequalities in the literature and fractional digit integral operators are introduced. In the next section, Reverse Minkowski, Hadamard and Simpson type inequalities are obtained by using ABK-fractional integral, Katugampola fractional integral and Atangana-Baleanu fractional integral operators. For the findings obtained, various results supporting the results available in the literature are given with the special selection of the parameters.