CRJ-700 captain reported a near midair collision with another aircraft that was not following ATC instructions. The Captain took evasive action to prevent a collision.

Narrative

In general; we were on a modified ZZZZZ arrival; with ATC issuing non-standard vectors/decent from what was published. While transitioning from the arrival (i.e. heading North) then we were basically given Westerly vectors and descents to 6000'. At some point; we were given direct to ZZZZZ and descend and maintain 4000'. During this process we could hear ATC and another Aircraft arguing (for several minutes) over altitudes and proper procedures transitioning via Approach Controls - Area of Responsibility. Ultimately; the aircraft in question was not following ATCs instructions or talking to anyone at all?! Moreover; as we were en route to both our next fix/altitude we also had to be cognizant (slow down) to meet the Class Bravo shelf speed restriction of 200 kts. Additionally; the Sun was essentially setting directly in our primary field of view with ample haze. ATC did advise us of said traffic; however between the Sun; and the Haze we could not acquire them in a timely manner. Ultimately; by the time we were approaching our 4000' I was getting a Traffic Alert of ~400' and closing fast with an aircraft that was not complying with ATC instructions. At that moment; I exercised my Captains Authority and chose to deviate altitude with a climb of 400-500' and right turn between 15-20 degrees. I advised the First Officer to notify ATC of the evasive maneuver; and we continued to ZZZ with no further issues.Suggestion: With great humility; I believe I made a sound decision given the circumstances at hand. With that being said perhaps a more defined transitioning corridor for civilian GA traffic might alleviate the preponderance of similar Traffic concerns. Or ATC could have vectored us around the potential traffic.