Integral inequalities for (α_1,m)-convex functions via Caputo-hybrid and Atangana-baleanu fractional integral operators

In this thesis study, various inequalities for 〖(α〗_1,m)-convex functions were examined and Hölder, Power Mean and Young inequalities were used in the process of obtaining the results. In the first part of the thesis, the broad history of inequalities is discussed, in the second part, definition theorems and examples are given, in the third part, information about Caputo-Hybrid and Atangana-Baleanu fractional integral operators is presented, in the fourth part, using existing lemmas, new inequalities regarding 〖(α〗_1,m)-convex functions have been obtained. Discussion and results are given in the fifth section. The main goal of this thesis is to examine 〖(α〗_1,m)-convex functions from a broad perspective and to reach new upper limits for inequalities of this type by obtaining new inequalities with these functions.