Air carrier First Officer reported engine control malfunction inflight.

Narrative

After a normal authrottles takeoff roll out of ZZZ; we climbed out and I placed the aircraft in the command bars. Soon after takeoff I observed the auto throttles were not on. After they were re-engaged; and while still pitching up for a climb in the command bars; I could feel and hear less power and noticed that the throttles were not full forward. This was confirmed on the EICAS so I manually moved throttles forward to full power. Even with significant back pressure it was difficult maintain altitude and keep climbing; especially with the bank commanded by the programmed SID and the lag between power application and airspeed increase. Not wanting to approach stick shaker or any possible stall; I initially held back from overly aggressive back pressure on the yoke and in that time we briefly didn't climb and lost a little altitude. Subsequently; and with now effective full power and flap retraction; the aircraft climbed normally; and FMS speeds now on; the speed tape showed 200 kts. with an intervention needed to get it to 250 kts. All this coincided with the re-appearance of Right FADEC fault on the CAS. During the climb; the aircraft was banking and power having rolled back; my First Officer called for the controls. However with the current altitude and having added sufficient power manually; I made the decision that exchanging controls in that vulnerable flight situation would only exacerbate things and delay our current trend which was of increasing power and airspeed. Out of 10;000 ft. the aircraft did not speed up to 300 kts. as it usually does; so I had to intervene 300 kts. for the now normal climb. Once we climbed into Mach speed regime the aircraft was able to maintain normal climb and eventually cruise speeds with no intervention. Though it may or not have relevance the Right FADEC fault had been persistent on the previous leg; and had to be cleared at ZZZ by going dark (rebooting); was also persistent all the way to ZZZ1. The rest of the flight was normal and uneventful. At ZZZ1 I wrote up the aircraft with guidance from Maintenance.