You can store an IP address in an INT UNSIGNED (4 bytes) which is of course much more efficient and faster than a CHAR(15).
MySQL has two built-in functions: INET_ATON() and INET_NTOA(). These two functions are used allover the place in any TCP/IP stack implementation or even application.
The INET_ATON() function converts Internet addresses from the numbers-and-dots notation into a 32-bit unsigned integer, and INET_NTOA() does the opposite.