Loss of power

Okay, the best way I know to explain how the vehicle is running is; when I first start it cranks and turns over strong but once started it immediately start to sputter and will eventually shut off if I don't give it some gas. I usually give it gas for a second then throw it in to drive and take off hoping I don't have to wait on any other cars going by because it will stall before I can pull off. It also will shut off if sitting at a red light or sitting still for too long it drives and sounds like it's not getting power or fuel somewhere but have done everything I know to do at this point. I have put on new alternator, changed out all plugs and wires, brand new battery, replaced fuses, and replaced several vacuum hoses. Thank you and have a blessed day!