The basic premise in the Japanese manga/anime Doraemon is that the titular character - a robot cat from the 22 century - was sent to the past to help Nobita Nobi to improve his future. In the first episode of the show, Nobita grandson Sewashi Nobi specifies that due to Nobita poor grades in school he meet many failures in his life, causing his descendants a lot of problem.
Doraemon was sent to the past so that Nobita could improve and become a better person. Based on many references in the show, apparently the future did indeed change - Sewashi states that Nobita was originally going to get married to "Gian" sister Jaiko but now the future shows him married to Shizuka instead.
Given these premises, it seems that time travel can change the present/future if the past is changed.
Yet every single other instance of time travel in the show seem to end up in a stable time loop... Here are just some example that come to mind:
- a coin is stolen from an house, no sign of infraction. Suneo points out that the only one able to perform such feat would be Doraemon using his Anywhere Door. Doreamon proceedes to go to the past to see what really happened, but when he find nothing he decides to take the coin to avoid it being stolen. He quickly realizes he just caused the coin disappearance.
- Nobita's parents have a argument on who of them proposed to the other, each one claiming it was the other. Nobita and Doraemon go to the past to check, they end up causing the issue (afraid that Nobita parents would never get together, Doraemon uses a trick that end up making each of them think it was the other who first proposed)
- Nobita hears a tale from his dad - when he was young he meet a weird girl that gave him some chocolate. Wondering on the identity of the girl, Nobita and Doraemon use the time machine again. Due to some weird series of events, Nobita ends up to be the one his young dad saw in the first place
- In another episode Nobita causes a problem by sending to future Doraemon a picture of them together - this makes Doraemon worry since he was originally yellow and seeing the photo (he is currently blue) could cause his future self a trauma and change history. At the same time he also states to remember something that "made him happy" the day he was born. Nobita and Doraemon manage to recover the photo, but the attached letter that Nobita sent with it ends up being the something that made future Doraemon happy and he remembered all along.
- Even what seems to be the only episode where story risk to be changed actually becomes a sort of loop. In "Nobita disappeared?" Nobita travels to the past to help his future father to pursue his dream as an artist. In doing so, he seems to change history so that his father would never marry his mother, and Doraemon fears that when the "ripple effect" in time flow would catch up, Nobita would disappear from existence. Yet, the problem basically solves itself and his father end up meeting his mother anyway (to the point it almost seems they actually caused it in the first place - Nobisuke meets Tamako while leaving Kaneko house and probably would never have been there if it was not for Nobita interference)
- the plot of the movie "Doraemon: New Nobita's Great Demon—Peko and the Exploration Party of Five" basically hinges around a loop. During the last "battle" in the movie, Shizuka uses one of Doraemon gadget to force a loop, making their future versions from the next day come back with the time machine to help them. This end up in two Gian, Suneo, Shizuka and Nobita. In doing so, Shizuka fulfills a prophecy about the number of heroes that would "save the day"
I could make some more examples but it should be clear by now. Every time Doraemon and Nobita use the time-travel machine apparently they end up in a stable time loop where all the consequences of their action where already in place from the start. All seems to point to a "Destiny is already written" trope, and yet the show premise is that Nobita managed to change his future.
I am therefore asking - outside of the obvious case of Nobita future, are there any actual example of future/past event being changed because of time travel in the show? I am aware that multiple episodes mention a "Time Police" which duty apparently is to prevent people from messing with history, but every instance I could think of has just the police preventing people from abusing time travel (for example poachers hunting dinosaurs) than actually preventing time changes.