That is a large frame Martini action that has been converted into a single shot handgun. However the cartridge is an oddity in that it is longer than a 7.62x39 but shorter than a 7.62x54. Another thing is that the cartridge appears to be rimless, the basic design of the Martini is for use of a rimmed cartridge. The extractor can be modified by cutting off one leg of the extractor and adding a spring plus a pivot pin but that is complicated without a shop.
Do you know how to disassemble the Martini action? If so, check the firing pin and firing pin hole, see if the firing pin has been turned down and had a bushing installed in the bolt. That will tell you if it has been converted to smokeless powder. If no bushing, it is still set up for black powder. This should tell you more about the cartridge. It could be that a rim was cut off in the casting which might make it a 47 or so rather than a 45. Then it is probably a British 8x47 R or something on that order.