Celoxis is an Indian enterprise grade project management solution, available in cloud and on-premise. Cloud service is priced at $25/user/mo, while a self-hosted edition of Celoxis is available at $450 per user (a one-time fee). It's not clear if source code for it is available, but most likely that's not the case, as Celoxis TOS clearly prohibits any efforts to "reverse assemble or otherwise attempt to discover any source code". Celoxis reviews are available via PCMagazine and other publications. Native apps for Android and iOS are not available, though company Wikipedia page states that Celoxis can be accessed and worked with from smartphones. If you are looking for a free Celoxis alternative, available both in cloud and on-premise, with access to source code and native mobile apps, take a close look at Bitrix24.
* Please note that the information may have changed since the publication. For current prices and features please visit Bitrix24 pricing page.