Some inequalities on conformable derivatives

Fractional analysis has emerged from the order of fractional numbers to derivatives by generalizing the concepts of derivative and integral . The only thing that fractional derivatives have in common with the classical derivative is that they are linear. The derivative of the multiplication and division of two functions, the chain rule and many other features do not comply with the classical derivative. Therefore, a new definition was made based on the classical derivative definition and providing the properties of the classical derivative. This relatively new definition which is called as the comformable derivative, has brought a new perspective to many branches of mathematics. The theory of inequalities is a concept that has the potential to develop and expand in mathematics and other sciences. In this thesis, we aimed to transfer some inequalities in literature to conformable derivatives. This thesis on inequalities in conformable derivatives consists of four chapters. In the first section, some existing inequalities in the literature are expressed. In the following section, information regarding the fractional derivative and conformable derivative is given, and the lemma and theorems required for our thesis are expressed and proved. In the next chapter, Chebyshev, Wirtinger, Jensen and Grüss-type inequalities are expressed and proved by using the conformable derivative. In the final chapter, a summary of this thesis is presented.