Currently, there is no software specifically designed for academic writing, but there is quite a bit of software that was designed for fiction writing that can be used for academic writing.
Writing software is typically designed for long-form--books and articles, but it can be used for papers or any writing.
Why writing software has grown in popularity:
Scrivener was originally developed for fiction writing. Increasingly it is the most popular writing software for academics.
Scrivener must be purchased, once. The price is reasonable; updates are typically free. Try it before you buy it! The free trial is for a generous 30 uses or opens, not 30 days. Scrivener is downloaded onto a particular computer and Scrivener-produced files can be stored in the Cloud.
Olin Library offers workshops at least once a semester. (Graduate students: contact me if you would like a customized Scrivener workshop offered in your department). I'm usually available for one-on-one meetings to help with Scrivener, or for workflow & productivity consultations, or if you have questions about alternatives to Scrivener.
Recommended resources for teaching yourself Scrivener: