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Yor's generalized meander is a temporally inhomogeneous modification of the$2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which theinhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce thenon-colliding particle systems of the generalized meanders and prove that theyare the Pfaffian processes, in the sense that any multitime correlationfunction is given by a Pfaffian. In the infinite particle limit, we show thatthe elements of matrix kernels of the obtained infinite Pfaffian processes aregenerally expressed by the Riemann-Liouville differintegrals of functionscomprising the Bessel functions $J_{\nu}$ used in the fractional calculus,where orders of differintegration are determined by $\nu-\kappa$. As specialcases of the two parameters $(\nu, \kappa)$, the present infinite systemsinclude the quaternion determinantal processes studied by Forrester, Nagao andHonner and by Nagao, which exhibit the temporal transitions between theuniversality classes of random matrix theory.Comment: LaTeX, 35 pages, v3: The argument given in Section 3.2 was  simplified. Minor corrections were mad

Infinite systems of noncolliding generalized meanders and Riemann–Liouville differintegrals