  In this article, Lie symmetry analysis is used to investigate invariance
properties of some nonlinear fractional partial differential equations with
conformable fractional time and space derivatives. The analysis is applied to
Korteweg-de Vries, modified Korteweg-de Vries, Burgers, and modified Burgers
equations with conformable fractional time and space derivatives.
  For each equation, all of the vector fields and the Lie symmetries are
obtained. Moreover, exact solutions are given to these equations in terms of
solutions of ordinary differential equations. In particular, it is shown that
the fractional Korteweg-de Vries can be reduced to the first Painlev\'{e}
equation and to fractional second Painlev\'{e} equation. In addition a solution
of the fractional modified Korteweg-de Vries is given in terms of solutions of
fractional second Painlev\'{e} equation.
