Not all GMs decline immediately after 35. Anand is 46 and still right at the top. His peak rating came at age 41 and he held on to his world champion title until age 43 (when he lost to Carlsen).
Viktor Korchnoi gave his expert opinion that most chess grandmasters hit their peak around age 40, maybe a little after. He also tried to analyze what gave various people the drive to work hard enough to become a grandmaster.
Also, Anand would arguably be world champion right now if he had the stamina. His knowledge of the game is probably the deepest of anyone, but he runs out of energy as th game progresses.
Physical fitness is given a lot of attention by players at the very top of chess. Here is a quote from an article that talks a bit about it.
“Anand has been pretty active as well,” says the Bad Sodener Zeitung. “He bought a season ticket for the swimming pool in Bad Soden and swam about 1000 metres per day. He would also run 10km every day and has also been spotted on a bicycle in the beautiful hills around Bad Soden. He lost about six kilos this summer. Most of the time, though, Anand prepared for the match in the Chess Tigers Training Centre with his seconds.”
Also, Anand would arguably be world champion right now if he had the stamina. His knowledge of the game is probably the deepest of anyone, but he runs out of energy as th game progresses.