Hermite-hadamard inequalities for ψ-Hilfer fractional and conformable fractional integrals

This thesis study is on Hermite-Hadamard inequalities for Ψ-Hilfer Fractional integrals and Hermite-Hadamard inequalities for Conformable Fractional integrals, respectively, based on new midpoint-type and trapezoidal-type inequalities. The study consists of five sections, the first part of which is an introduction. The second part consists of some inequalities, definitions, and theorems necessary for the study. Additionally, in the second part, the proof of the Hermite-Hadamard inequality, inequalities for Riemann-Liouville Fractional integrals, some inequalities for Ψ-Hilfer Fractional integrals, and finally some inequalities for Conformable Fractional integrals are presented. In the third part, new midpoint-type and trapezoidal-type Hermite-Hadamard inequalities for Ψ-Hilfer fractional integrals are provided using the boundedness of the second derivative of the function ξ. Similarly, in the fourth part, new midpoint-type and trapezoidal-type Hermite-Hadamard inequalities for Conformable Fractional integrals are given and supported with examples. In the fifth and final part, conclusions are drawn, and some suggestions for future studies are given.