Let's take a look at the root adjectives of these adverbs!
Fortunately - Fortunate. To be fortunate means to have fortune or luck.
Hopefully - Hopeful. To be hopeful means to have hope.
Thankfully - Thankful. To be thankful means to have gratitude or to be in giving of thanks.
1. My sister was sick. Thankfully, she's bounced back from the illness and is well now.
- We can be THANKFUL that she is well! So we can use the word THANKFULLY.
2. My sister was sick. Fortunately, she's bounced back from the illness and is well now.
- We can also say that it is FORTUNATE that she is well! So we can use the word FORTUNATELY.
These two have a similar meaning and use the same context. That is, we KNOW that your sister is well now!
However, if we use HOPEFULLY, we change the meaning and the context:
3. My sister was sick. Hopefully, she's bounced back from the illness and is well now.
- In this case, we would not know if your sister is well yet! We could use HOPEFULLY if she is sick and we are HOPEFUL that she WOULD be well again. If we know that she is already well, we do not have to be hopeful!
I hope this was helpful! :)