Being in medication of arthritis, what are the exercise that could help. (home exercise preferred)
This is the wrong place to ask for that information. Only your doctor can tell you that, because you could hurt yourself further if you take advice from the internet and do an exercise which isn't good for you. I do know that exercise can help with arthritis, so maybe your doctor would even be willing to send you for one or two physical therapy appointments if you need that help to choose some exercises you can do. I hope you find a program you like.
Stretching is great. This will help loosen you up for when you workout. There are probably a few workouts on youtube - same with stretching.....Well, I just checked and there are a ton of stretching and workouts that you can do from sitting positions and such if that is your limit. Check out arthritis workouts or stretching.
And if you aren't in the best shape, have an Epsom Salt balt afterwards.
I too have arthritis and I find that yoga and tai chi are great...both low impact and relaxing...you get a lot of stretching which is good for arthritis.