Inequalities for different types of convex functions via Atangana - Baleanu fractional integrals

The possibility of the existence of fractional-order derivatives, as posed by L'Hôpital to Leibniz, did not receive much attention in the application of fractional analysis until the last 50 years. However, it has gained momentum in recent years due to its potential to provide a new perspective on modeling non-local problems and its usefulness in addressing various challenging real-world problems. This has led to more realistic calculations in disciplines such as mathematics, physics, chemistry, biology, economics, and engineering. In recent years, fractional derivatives and integrals have been studied rapidly, particularly in conjunction with inequality theory. Various integral inequalities have been discovered and are expected to continue being explored in more general forms. This thesis focuses on the integrals corresponding to local and non-singular fractional derivatives, which were introduced into the literature by A. Atangana and D. Baleanu in 2016. The thesis provides definitions, theorems, and concepts related to the topic, along with an extensive literature review. By utilizing Atangana-Baleanu fractional integrals, new Hermite-Hadamard type inequalities are derived for certain types of convex functions.