Ed Bearss, in Rebel Victory at Vicksburg, spends portions of several chapters discussing the Arkansas. This book covers the early operations around Vicksburg, including the actions of Farragut's and Davis' fleets, and the Arkansas. There may be other books specifically on the Arkansas, but this is the only one that I've read. Hope this helps.

We used to carry a book published by Hill College Press entitled THE SAGA OF THE CONFEDERATE RAM ARKANSAS, written by Tom Parrish. We no longer have copies for sale, but you might be able to find a copy on bookfinder.com.
Clark