jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pIn this work we derive three sets of non-perturbative fragmentation functions, with uncertainties, for jats:italicB</jats:italic>-hadrons, jats:italicJ</jats:italic>/jats:italicψ</jats:italic>’s and muons resulting from semileptonic jats:italicB</jats:italic> decays. All three sets are with next-to-next-to leading order accuracy and include next-to-next-to leading logarithmic soft gluon resummation. The novel feature of these new sets is that they are fully consistent with our formalism for next-to-next-to leading order (NNLO) calculations for final states with identified jats:italicB</jats:italic>, jats:italicJ</jats:italic>/jats:italicψ</jats:italic> or a jats:italicμ</jats:italic>. We employ the fragmentation functions derived in this work to make state of the art predictions for such final states in jats:inline-formulajats:alternativesjats:tex-math$$ t\overline{t} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mit</mml:mi> mml:mover mml:mit</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> events at the LHC. A special emphasis is placed on observables sensitive to the top quark mass. The present work opens the door for many LHC applications, like, open jats:italicB</jats:italic> production or jats:italicB</jats:italic> production in association with bosons.</jats:p>