I read this comic since I was 10 years-old.
As you know, Doraemon is a story with no ending, but this small story is about the “last episode” of the famous cartoon.
Someone made this story (finally I know the name, Nobuo Sato) and uploaded it to his homepage, and it is now widely spread all around Japan through the internet.
Here it goes. Happy reading :)

 

Doraemon’s Short Stories (Book 1)

Doraemon is sent back in time by a young boy named Sewashi Nobi to improve the circumstances of his grandfather, Nobita,
so that his descendants may enjoy a better future. In the original timeline, Nobita experienced nothing but misery and 
misfortune manifested in the form of very poor grades and bullying throughout his life. 
In order to alter history and better the Nobi family's fortunes, Sewashi initially wanted to send a super-robot to 
protect Nobita, but with his meager allowance he could only afford an imperfectly-made factory-rejected toy: an 
anthropomorphic robot cat called Doraemon.
Doraemon has a pocket called "4th-Dimensional Pocket" from which he produces gadgets, medicines, and tools from the future. 
Thousands of gadgets have been featured in the series with such as the "Hop-copter/ Takke Copter", a small head accessory 
that allows flight and the "Anywhere Door/Dokodemo Door," a door that opens up to any place the user wishes.
Nobita's closest friend is Shizuka Minamoto, who also serves as his romantic interest. They are tormented by the bully 
Takeshi Goda/Gouda, nicknamed "Gian," and the cunning and arrogant Suneo Honekawa/Hunekawa. 
A typical story consists of Doraemon using one of his gadgets in order to assist Nobita in various ways, often causing more
trouble than he was trying to solve.  ;)