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.
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