Some properties of fractional burgers equation

The fractional generalization of a one-dimensional Burgers equation (Formula presented.) with initial conditions φ(x,0) = φo(x); φt(x,0) = ψo(x), where φ = φ(x,t) ∈ C2(Ω); φt ≡ ∂φ/∂t; aDpx is the Riemann-Liouville fractional derivative of the order p: Ω = (x,t): x ∈ E1,t, > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf-Cole transformation are discussed.