Provides tools for modelling, forecasting and visualising long-memory functional time series with the functional autoregressive fractionally integrated moving-average model. The model is fitted in three steps, each of which can also be used on its own. First, the memory parameter is estimated from the leading principal component scores, for example by local Whittle or by bias-corrected local polynomial Whittle with noise. Second, the autoregressive and moving-average orders of the fractionally differenced curves are selected by a functional information criterion, functional Box-Jenkins or cross-validation. Third, the operators are estimated. The point forecasts come with conformal prediction bands that quantify their uncertainty. Visualisation tools include improved rainbow plots and plots of the fitted model and its forecasts.