  The paper is concerned with the time-periodic (T-periodic) problem of the
fractal Burgers equation with a T-periodic force on the real line. Based on the
Galerkin approximates and Fourier series (transform) methods, we first prove
the existence of T-periodic solution to a linearized version. Then, the
existence and uniqueness of T-periodic solution to the nonlinear equation are
established by the contraction mapping argument. Furthermore, we show that the
unique T-periodic solution is asymptotically stable. This analysis, which is
carried out in energy space $ H^{1}(0,T;H^{\frac{\alpha}{2}}(R))\cap
L^{2}(0,T;\dot{H}^{\alpha})$ with $1<\alpha<\frac{3}{2}$, extends the
T-periodic viscid Burgers equation in \cite{5} to the T-periodic fractional
case.
