Fractional differential generalization of the Burgers hierarchy

We generalize the Burgers hierarchy to the case of an arbitrary positive fractional order. We introduce a nonlinear fractional differential operator generated by a fractional power of the recursion operator of the original hierarchy. We show that, as in the integer case, the fractional differential equations of the generalized hierarchy are linearized by the Cole–Hopf transformation. In particular, the fractional differential generalization of the Burgers equation is transferred by this transform into a fractional differential superdiffusion equation. We find recursion operators for these equations and construct higher symmetries, local and nonlocal, including fractional differential ones.