► Fuzzy fractional H-differentiability is provided. ► The fuzzy Laplace transform of fuzzy fractional derivatives is obtained. ► Some new basic properties of fuzzy Laplace transforms are derived. ► Fuzzy fractional differential equations is solved using mentioned method. This paper deals with the solutions of fuzzy fractional differential equations (FFDEs) under Riemann–Liouville H-differentiability by fuzzy Laplace transforms. In order to solve FFDEs, it is necessary to know the fuzzy Laplace transform of the Riemann–Liouville H-derivative of f, RL D a + β f ( x ) . The virtue of L RL D a + β f ( x ) is that can be written in terms of L f( x). Moreover, some illustrative examples are solved to show the efficiency and utility of Laplace transforms method.