On new inequalities involving fractional integrals

In this thesis, we first present a lemma for twice differentiable functions to derive trapezoid and midpoint inequalities. Utilizing this lemma, we establish several inequalities for functions whose second derivatives in absolute value are convex, employing Riemann-Liouville fractional integrals. These results extend the midpoint and trapezoid inequalities involving Riemann-Liouville fractional integrals that were discussed in previous studies. Furthermore, we develop Hermite-Hadamard type inequalities for functions with second derivatives whose absolute values are convex. To achieve this, we derive an identity using Green's function. Using this identity, we obtain our main results.