Abstract
In this paper, we construct the Backlund transformations and the super-position formulas to the constant coefficients local fractional Riccati equation for the first time. Next, by means of the Backlund transformations and seed solutions which have been known. in [X. J. Yang et al., Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fandam. Inform. 151(1-4) (2017) 409-417], we can get a class of exact solutions to the third-order modified KdV equation on the fractal set. These new type solutions can assist us to review different nonlinear phenomena better, which had been modeled via local fractional derivative.