  Currently, much interest is drawn to the analysis of optical and matter-wave
modes supported by the fractional diffraction in nonlinear media. We predict a
new type of such states, in the form of domain walls (DWs) in the two-component
system of immiscible fields. Numerical study of the underlying system of
fractional nonlinear Schroedinger equations demonstrates the existence and
stability of DWs at all values of the respective Levy index (a < 2) which
determines the fractional diffraction, and at all values of the XPM/SPM ratio b
in the two-component system above the immiscibility threshold. The same
conclusion is obtained for DWs in the system which includes the linear
coupling, alongside the XPM interaction between the immiscible components.
Analytical results are obtained for the scaling of the DW's width. The DW
solutions are essentially simplified in the special case of b = 3, as well as
close to the immiscibility threshold. In addition to symmetric DWs, asymmetric
ones are constructed too, in the system with unequal diffraction coefficients
and/or different Levy indices of the two components.
