Symmetry analysis of reaction diffusion equation with distributed delay

•This paper gives at first the evolutionary infinitesimal vector field of Delay RDE.•We give a number of group-invariant solutions corresponding to vector field.•Main Method: Classical generalized symmetries of differential equation theory.

This paper study the reaction–diffusion equation with distributed delay from the Lie group theoretic point of view. We give at first the evolutionary infinitesimal vector field vv and a number of group invariant solutions corresponding to vv by general symmetry group theory.