Yor's generalized meander is a temporally inhomogeneous modification of the
$2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the
inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the
non-colliding particle systems of the generalized meanders and prove that they
are the Pfaffian processes, in the sense that any multitime correlation
function is given by a Pfaffian. In the infinite particle limit, we show that
the elements of matrix kernels of the obtained infinite Pfaffian processes are
generally expressed by the Riemann-Liouville differintegrals of functions
comprising the Bessel functions $J_{\nu}$ used in the fractional calculus,
where orders of differintegration are determined by $\nu-\kappa$. As special
cases of the two parameters $(\nu, \kappa)$, the present infinite systems
include the quaternion determinantal processes studied by Forrester, Nagao and
Honner and by Nagao, which exhibit the temporal transitions between the
universality classes of random matrix theory.