  Of concern are traveling wave solutions for the fractional
Kadomtsev--Petviashvili (fKP) equation. The existence of periodically modulated
solitary wave solutions is proved by dimension breaking bifurcation. Moreover,
the line solitary wave solutions and their transverse (in)stability are
discussed. Analogous to the classical Kadmomtsev--Petviashvili (KP) equation,
the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line
solitary waves of fKP-I equation are transversely linearly instable. We also
perform numerical experiments to observe the (in)stability dynamics of line
solitary waves for both fKP-I and fKP-II equations.
