Integral inequalities for different kinds of convex functions via conformable fractional integrals

In this thesis, convex functions that has a close relation to inequality theory and kinds of convexity have been introduced. Some properties have been placed by starting with the relationship between definition of convex functions and means. Primarily, the concepts of fractional derivative and fractional integrals have been mentioned and later the definition of conformable fractional derivative and integrals have been given. The basic concepts of conformable fractional derivative and integrals have been recalled. Some inequalities that have been proved via conformable fractional integrals which have been presented in the literature. In the findings section, two new integral identity that are include conformable fractional integrals have been established. Finally, some new integral inequaliies have been obtained via conformable fractional integrals and some integral inequalities such as Hölder and Power-mean integral inequalities. Keywords: Hermite-Hadamard type inequalities, Hölder inequality, Power-mean inequality, convex functions, conformable fractional integrals.