In this article, we first obtain an identity that we will use throughout the article. With the help of this equality, new inequalities involving a real parameter are established for Riemann–Liouville fractional integrals. For this purpose, properties of the differentiable convex function, Hölder inequality, and power-mean inequality are used. In addition, new results are established with special choices of parameters in all proven inequalities. Our results are supported by examples and graphs. It is shown that some of these results generalize the trapezoid type and Newton-type inequalities.