Giorgos,
There are some discrepancies in the information you provide, that make it difficult to pin down the model and year. Douglas were not selling motor cycles in 1915 with drum brakes and chain final drive. They did however have a machine called the 2-3/4hp that was two-speed with chain drive to the transmission, and belt drive to the rear wheel. The economy model did not have a kick starter or clutch, though these could be had on a more deluxe version. It is possible that someone 'modernized' your machine with all chain drive and improved brakes. The original brakes (if it is a 2-3/4hp) would be a brake block in the rear belt rim, and a stirrup brakes working directly on the front rim. You should see a pivot lug on the rear chain stay tube, and small clips brazed to the front forks as remnants of the original system.
By the way if it is a 2-3/4hp, the petrol tank Brett has listed which you inquired about is not going to fit your frame. The petrol tank for a 2-3/4hp is not as tall, and is suspended from the top frame tube where as the EW petrol tank mounts from the bottom. The serial numbers for the engine, frame, and transmission will definitively identify and date the major components.
-Doug