Opial type integral inequalities and applications

The main purpose of this thesis is generating new inequalities and their generalizations for conformable fractional integrals by the help of Opial type of inequalities. In chapter 2, the basic concepts were given which used in thesis. For integrals, we used some basic inequalities and definition. In the third chapter, it's given the basic proof of Opial Inequality and also its other proofs which was made by different mathematicians. In addition, this chapter it's given in detail, some generalizations and applications of Opial type inequalities in the literature for the last 50 years. In the fourth chapter, some new Opial type inequalities and their generalizations are obtained for conformable fractional integrals. In Chapter 5, some useful results were achieved for conformable fractional integrals by using convexity. Finally in Chapter 6, which given the results of Opial type inequalities which contains two independent variables and their applications for conformable fractional integrals. In the last chapter which given the findings and the contribution to the literature. Keywords: Convexity, Opial inequality, Conformable fractional derivative, Conformable fractional integrals