  This work is dedicated to the quantization of the light-front Yukawa model in
D=1+3 dimensions with higher order derivatives of the scalar field. The problem
of the computing Dirac brackets and the (anti-) commutator algebra of
interacting fields in the presence of the constraints is discussed. The Dirac
method and the Ostrogradski formalism of the higher order derivatives are
exploited. The systematic method of obtaining the inverse of the functional
Dirac-Bergmann matrix with interactions and higher order derivatives is
introduced in two variants. The discussion of applications and details of these
two variants are conducted. The results of the quantization in the form of the
(anti-) commutator algebra are presented and analyzed with special regard to
the structure of the interactions for the light-front Yukawa model, which
includes the higher order derivatives.
