Fractional Captain reported a possible GPS jamming event that resulted in the aircraft slowly descending and veering off course and the autopilot disconnecting without any audible alert.

Narrative

We were cruise FL430; on Y436 between DIZNY and EBEAR (I think) and talking to JAX Center. We initially got a Crew Alerting System (CAS) Turn Coordinator; and a minute or so later; while my FO was reading from the Norm/Abnormal Checklist; we got mechanical malfunction on GPS2 CAS message. While my FO was reading the checklist for the mechanical malfunction message and we were discussing the issues; the plane started veering off course (to the right) and had begun a very slow descent (without any audible alerts telling us the autopilot had disconnected). The aircraft acted like it was lost... I immediately selected heading mode (the plane had begun a slow right turn off course). But; the plane did NOT respond to heading mode; so I immediately began hand-flying to get back on course (turning left) and recovering the lost altitude (roughly losing 300 feet; as I asked ATC to confirm). We alerted ATC of GPS jamming; asked for a heading on course to OGGRE (as the plane was still kind of lost). Once I got the plane under control and back to FL430; I asked ATC if there were any separation issues. He stated that there were no issues and that he advised us that he let the military know to stop doing what they were doing.