We demonstrate that it is possible to perform a fractional Fourier transfor
m of an incident pulse with a continuously variable degree of fractionality
, using a dispersive and nonlinear Ken: medium. This medium acts as a linea
r waveguide for the optical pulse if its intensity is small and if the refr
active index is nonlinearly time-dependently modified by a simultaneously l
aunched bright soliton. For optical pulses the dispersive and nonlinear med
ium is perfectly equivalent to a graded-index refractive medium for optical
beams. (C) 1999 Optical Society of America OCIS codes: 070.2580, 070.6020,
230.7370, 190.4360, 320.5550.