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We present a timing analysis of the 2015 outburst of the accretingmillisecond X-ray pulsar SAX J1808.4-3658, using non-simultaneous XMM-Newtonand NuStar observations. We estimate the pulsar spin frequency and update thesystem orbital solution. Combining the average spin frequency from the previousobserved, we confirm the long-term spin down at an average rate$\dot{\nu}_{\text{SD}}=1.5(2)\times 10^{-15}$ Hz s$^{-1}$. We also discusspossible corrections to the spin down rate accounting for mass accretion ontothe compact object when the system is X-ray active. Finally, combining theupdated ephemerides with those of the previous outbursts, we find a long-termorbital evolution compatible with a binary expansion at a mean rate$\dot{P}_{orb}=3.6(4)\times 10^{-12}$ s s$^{-1}$, in agreement with previouslyreported values. This fast evolution is incompatible with an evolution drivenby angular momentum losses caused by gravitational radiation under thehypothesis of conservative mass transfer. We discuss the observed orbitalexpansion in terms of non-conservative mass transfer and gravitationalquadrupole coupling mechanism. We find that the latter can explain, undercertain conditions, small fluctuations (of the order of few seconds) of theorbital period around a global parabolic trend. At the same time, anon-conservative mass transfer is required to explain the observed fast orbitalevolution, which likely reflects ejection of a large fraction of mass from theinner Lagrangian point caused by the irradiation of the donor by themagneto-dipole rotator during quiescence (radio-ejection model). This strongoutflow may power tidal dissipation in the companion star and be responsible ofthe gravitational quadrupole change oscillations.

On the timing properties of SAX J1808.4-3658 during its 2015 outburst