Some new type fractional inequalities

In this thesis, in which the fractional calculus is explained and some important fractional inequalities are examined, consists of four sections. In the first chapter, we introduce the fractional calculus and give information about the history of the subject. In the second chapter, we mention basic definitions and theorems. In the third chapter, we extend the Hermite-Hadamard inequality for convex functions using the Caputo and k-Caputo fractional derivatives, obtain some new theorems. In the fourth and the last chapter, we extend some inequalities for different type of convex functions using Caputo and k-Caputo fractional derivatives, we investigate and prove the theorems. Finally we give conclusions and suggestions.