Alex de Minaur loses to Jannik Sinner at ATP finals, Daniil ...

World number one and home favourite Jannik Sinner has begun his bid to win the ATP Finals for the first time with a 6-3, 6-4 defeat of tournament debutant Alex de Minaur.

Sinner, runner-up to Novak Djokovic in the prestigious year-ending tournament last year, dropped behind early in the first set but quickly hit back to dominate the contest.

The Italian, who won this year's Australian and US Open titles to open his grand slam account, completed victory with an ace.

Earlier in the Ilie Nastase Group American Taylor Fritz beat Russian Daniil Medvedev 6-4, 6-3.

Numerous spectators were dressed in orange or wore carrot costumes in honour of Sinner's symbol vegetable — and his hair colour.

Sinner showed no signs of nerves when he opened with an ace on the first point of the match and promptly held at love.

The Italian was broken in his second service game, though, but he responded by winning four straight games to take control as fans chanted his name on the changeovers.

It is the first time Sinner is playing at home since it was announced before his US Open title that he tested positive in two separate drug tests this year.

A decision to clear Sinner of wrongdoing was appealed by the World Anti-Doping Agency in September. 

A final ruling in the case is expected early next year.

Daniil Medvedev destroyed a racket against Taylor Fritz. (AP: LaPresse/Marco Alpozzi)

Earlier, US Open finalist Taylor Fritz frustrated Daniil Medvedev to the point that the Russian smashed his racket and was docked a point in a 6-4, 6-3 victory for the American.

Medvedev received two code violations from the chair umpire for his behaviour.

"I get angry, frustrated. This time completely with myself, not with anyone. Just with myself," Medvedev said.

The first set had been virtually dead even until the final game when Medvedev hit three double-faults to hand the set to Fritz.

Medvedev then went over to his bench in a fit of rage.

Medvedev first slammed his racket against the bench, which resulted in a slight dent. 

Then he banged the racket again on the hard court inside Inalpi Arena and mangled the frame into a twisty mess — prompting him to toss it behind him.

"I have this every day, day in, day out, since like two, three years. Every practice is a struggle. Every match is a struggle," Medvedev said. 

"Now I feel zero pleasure of being on the court."

Midway through the second set, Medvedev was docked a point after he was broken and lost his cool again.

Medvedev then acted as if he was going to return serve with his racket facing the wrong way — he held it with the butt of the racket and the grip facing Fritz. That drew whistles from the crowd and Medvedev changed the racket position just before Fritz served.

"I was like, 'Whatever, I lost the match. I don't care,'" Medvedev said.

Fritz wasn't bothered by Medvedev's behaviour.

"I was just laughing. I think he's really funny, to be honest," Fritz said. 

"Even when he's not playing me, he always cracks me up."

Fritz won long and memorable rallies at the start of each set, one that included 26 shots and another that lasted 30.

"It was huge," Fritz said. 

"I kind of just fought through … I thought I did a solid job showing him that I wasn't going to give him a lot of free points."

It was points like those that left Medvedev demoralised.

"Literally everyone can stay in the rally with me right now," Medvedev said.

Reuters/AP