By virtue of the left-sided fractional integral operators having exponential kernels, proposed by Ahmad et al. in [J. Comput. Appl. Math. 353:120-129, 2019], we create the left-sided fractional Hermite–Hadamard type inequalities for convex mappings. Moreover, to study certain fractional trapezoid and midpoint type inequalities via the differentiable convex mappings, two fractional integral identities are proven. Also, we show the important connections of the derived outcomes with those classical integrals clearly. Finally, we provide three numerical examples to verify the correctness of the presented inequalities that occur with the variation of the parameter $\mu$.