By applying exponential type $m$-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $\omega$ where $\omega$ and $|{\omega }^{\prime }|$ (or $|{\omega }^{\prime }{|}^q$with $q\ge 1$) are exponential type $m$-convex. Also, the results presented in this article provide generalizations of those given in earlier works.