  We report a comprehensive investigation and experimental realization of
spectral bifurcations of ultrafast soliton pulses. These bifurcations are
induced by the interplay between fractional group-velocity dispersion and Kerr
nonlinearity (self-phase modulation) within the framework of the fractional
nonlinear Schr\"{o}dinger equation. To capture the dynamics of the pulses under
the action of the fractional dispersion and nonlinearity, we propose an
effective `force' model based on the frequency chirp, which characterizes their
interactions as either `repulsion', `attraction', or `equilibration'. By
leveraging the `force' model, we design segmented fractional dispersion
profiles that directly generate spectral bifurcations \{1\}$\rightarrow$ \{N\}
at relevant nonlinearity levels. These results extend beyond the traditional
sequence of bifurcations \{1\}$\rightarrow$ \{2\}$\rightarrow$ \{3\} ...
$\rightarrow$ \{N\} associated with the growth of the nonlinearity. The
experimental validation involves a precisely tailored hologram within a pulse
shaper setup, coupled to an alterable nonlinear medium. Notably, we achieve up
to N=5 in \{1\}$\rightarrow$ \{N\} bifurcations at a significantly lower
strength of nonlinearity than otherwise would be required in a sequential
cascade. The proposal for engineering spectral bifurcation patterns holds
significant potential for ultrafast signal processing applications. As a
practical illustration, we employ these bifurcation modes to optical data
squeezing and transmitting it across a 100-km-long single-mode fiber.
