Praise be to Allah, and may peace and blessings be upon the Messenger of Allah, his family and companions. Now then:
As for the day on which you will travel before sunset, you must initially fast it, because you will be a resident at the beginning of it. Then, if you travel during it, you should complete your fast and not break it, taking into consideration the opinion of the jurists who forbid a fasting person from breaking his fast if he travels during the day. See Fatwa No. 128994. Regarding the opinions of the jurists regarding a traveler breaking his fast after starting his fast.
There is no blame on you for breaking your fast during your travel after you have started your travel, because Allah, the Most High, says (interpretation of the meaning): “But whoever among you is ill or on a journey – the same number (of days) must be made up from other days.” [Surat Al-Baqarah: 184]
When you reach your country, Libya, you must fast because your travel has ended. See Fatwa No. 375982.
And Allah knows best.