Emphasise the benefits. Discuss how the journey will benefit you, educationally, professionally and personally.
Assure them of your safety. Give them your itinerary and contact information. Promise regular updates and check ins while on the road.
Build their confidence in you. Demonstrate that you're responsible, reliable and capable of handling surprises and challenges.
Offer compromises. Propose a shorter journey, or offer regular check-ins. Find a compromise that addresses their concerns while allowing you to travel.
Be patient and understanding. Their worries may come from a place of love and concern. Listen to them and try to see things from their point of view.