Some inequalities associated with fractional integrals

Fractional derivatives and fractional integral notions were first raised by Liouville. The main source of this idea; fractional derivatives and fractional integral concept has emerged from the question: "Is there derivatives and integrals for only integers." Then, Euler dealt with fractional derivatives again and Leibniz, Euler, Lagrange, Abel, Liouville and many other mathematicians have begun to develop the fractional derivatives since 17th century as their pioneering work based on differential and integration to be generalized to fractional order. Arbitrary order differential and integration concepts are the notions which combine and generalize integer-order derivatives and n-fold integrals. Thus, this thesis consists of four chapters. In the first chapter, of how the concepts of fractional integral and fractional derivative is given. In the second chapter, all the necessary definitions and basic theorems for this study have been given. The third section, benefiting from the available data the findings summarized under three headings are given. In the fourth chapter, results and recommendations will be given.