In the TV series Two & a Half Men, Charlie and Alan are brothers, but there is no indication as to who is the elder. Even Wikipedia doesn't say anything about this. I have watched only season 1. So may be it is revealed in a later season. Who is the elder?
Quoting from Two and Half Men Wiki, in Season 7, episode 11 - "Warning, It's Dirty"
Evelyn reminds Charlie how forty years earlier, he had asked for a little brother for Christmas, which in contrast puts in doubt whether Alan was unplanned or not.
IMO, this proves that Charlie was the elder brother.
Charlie is the older brother. There are jokes in a number of episodes that establish this.
Also, the Two and a Half Men wiki does confirm this:
Dr. Alan Jerome "Al" Harper, DC, is a character from the CBS sitcom Two and a Half Men. Portrayed by Jon Cryer, Alan is the hapless and helpless biological father of Jake Harper, roommate and best friend of Walden Schmidt and the surviving younger brother of Charlie Harper.
The wiki lists the years of birth: Charlie: 1967, Alan: 1969.
According to the following quote from s08e08, Alan is 2 years younger than Charlie (the parts in italic I added for context, those are not part of the actual transcript):
Alan says: You're gonna leave me alone with her?
Charlie replies: Hey, I was alone with her for two years before you were born.
Source: transcript by springfieldspringfield.
In season 11, episode 13("Bite Me, Supreme Court"), during Evelyn's marriage with Matt, Evelyn says that this will be her first marriage without his sons. Someone says, what about her first ever marriage to which she replies, Charlie was in her stomach during the first marriage. Hence Charlie is older.