Integral inequalities for some different kinds of differentiable convex functions by using Atangana-Baleanu fractional integral operator

In this thesis, new integral inequalities are obtained for some different types of differentiable convex functions using the Atangana-Baleanu fractional integral operators, one of the important concepts of fractional calculus. The first section of the study provides general information about inequality theory and convex analysis. The second section, "Theoretical Foundations," introduces the basic concepts of inequality theory and convex analysis, and provides definitions of some well-known integral operators in fractional calculus. The third section, "Materials and Methods," addresses some integral inequalities found in the literature. Furthermore, some classical inequalities and integral identities used to obtain new integral inequalities are presented. The fourth section, which includes the research findings, includes some new integral inequalities involving the Atangana-Baleanu fractional integral operators and their proofs. The final section provides a general evaluation of the results.