There are several components to jet lag and it is worth considering each
It is difficult to get enough sleep when travelling even in the same time zone. Minimise the impact of factors such as light, noise, comfort and temperature. Do try out eye covers and ear plugs. Wear several layers of shirt/jumper so that you can add or remove them to reach the optimum temperature. Avoid the interest of the all night movies.
Sedatives can help but risk making you drowsy the next day. Nytol (diphenhydramine) is an antihistmine available at the chemist and the safer to use. Z drugs like zopiclone and valium derivatives such as temazepam are stonger, but are not a guaranteed and are only on prescription in the UK
Either keep to the new time and stay awake, which will produce a quicker adjustment, or take a short nap (maximum 3hrs) or consider staying on the old time if it is a brief trip. Melatonin is the body hormone that controls sleep, but only helps some people and is prescription only in the UK.
This can be overlooked. The digestive system also has a body clock, which can be anticipated with snacks. If ignored your stomach can wake you with a need to eat or empty your bowels. Eating itself can induce sleep and bowel activity so consider this before you are meant to go to sleep. When you wake up, and it is too early, consider a snack and emptying bowels and bladder before a quiet activity such as reading