I don't know if we have any inbuilt API for sending SMS to mobile phone from Mainframes.
Generally SMS are sent to mobile phone via APIs made available from SMS gateways.
There are number of SMS gateways available. They provide number of APIs that suits your application . for example HTTP API in which you need to format and send HTTP request to their server and inturn they will relay your SMS.
Another kind of API which can be useful is FTP. In one of my application, I have integrated SMS functionlity with my application using FTP api provided by the SMS gateway. ( I think mentioning the SMS gateway might not be allowed in the forum).
All I had to do is to sent a properly formatted text file which contains senders name, receivers mobile number and othe authentication info.
to their FTP dropbox and they delivered the SMSs .
If we have any inbuilt functions to send SMS please let me know. It will be interesting to know this piece of information.