Integral inequalities and applications for generalized fractional integral

The aim of this thesis is to transform the inequalities, which express various fractional integral, one form by combining and generalizing. The dissertation is cinssi of six part. the first part there are informations about; inequalities, convexion, the Hermite-Hadamard inequalities revealed by the functions which has character and the progress of fractional integral form naissance until today. In the second part there are definitions, connections between the notions, which giving information about naissance and progress in the first part and also definitions, theorems used in the dissertation. In the third part, beginning of our original results, we showed the Hermite-Hadamard inequalities, an important point in literature; generalization term of fractional integral and which fractional integrals are generalized by specific function selection. This generalization made three different form by changing limits. Every generalization has different results. In the fourth and fifth parts given the generalized fractional integral express for the Trapezoid and Midpoint type of inequalities, revealed by the Hermite-Hadamard inequalitie's left and right sections, first and second degree of differentiable functions. In the six part, given fractional integral and its generalized form result of express of algebraic expression of the Simpson inequalities which is the Simpson method used in numerical analysis, providing microscopic scale of result.