In the literature, the left-side of Hermite–Hadamard's inequality is called a midpoint type inequality. In this article, we obtain new integral inequalities of midpoint type for Riemann–Liouville fractional integrals of convex functions with respect to increasing functions. The resulting inequalities generalize some recent integral inequalities and Riemann–Liouville fractional integral inequalities established in earlier works. Finally, applications of our work are demonstrated via the known special functions.