  We prove variation and oscillation $L^p$-inequalities associated with
fractional derivatives of certain semigroups of operators and with the family
of truncations of Riesz transforms in the inverse Gaussian setting. We also
study these variational $L^p$-inequalities in a Banach-valued context by
considering Banach spaces with the UMD-property and whose martingale cotype is
fewer than the variational exponent. We establish $L^p$-boundedness properties
for weighted difference involving the semigroups under consideration.
