Give FileRun a try in your mobile browser, you will be impresed by how well it works without the need for an app.
See our Android and iOS recommended apps.
FileRun comes with its own WebDAV server, so you can also try out any other compatible client program.
See this page for information on how to connect via WebDAV.
There are two options, "Nextcloud" and "Owncloud" and they are the result of open-source projects with the same name.
Note that you will need to enable the API in FileRun's control panel in order to use the apps.
Latest supported version for Nextcloud apps: 3.13
Latest supported version for ownCloud desktop app: 5.2.1