When you bought the Mini how did you set it up ? PDFs are not stored in the cloud, so an iCloud restore wouldn't have copied them onto it, and an iTunes restore would have looked to pick them up from the Books section of the computer's iTunes library (iBooks app if using an up-to-date Mac).
Have you got the PDFs on your computer ? Or have an old iPad with them still on it ? If you have you can sync them to your Mini from your computer (if you only have them on a different iOS device then connect it to your computer's iTunes and try File > Devices > Transfer Purchases, and if using a Mac with iBooks on it then do File > Move Books From iTunes in iBooks ; they should then then hopefully show for selecting and syncing to the Mini)