He lives in a city where there are no other Muslims; how should he pray Jumu‘ah?
In order to establish Jumu‘ah prayer it is sufficient for there to be three men who are residents. Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The most correct scholarly opinion is that the number that is sufficient for Jumu‘ah is three: an imam to deliver the khutbah, a mu’adhdhin to give the call to prayer, and a worshipper to answer the call.
End quote from Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 13/831
Please see also the answer to question no. 7718
The Muslims who are resident in non-Muslim countries are obliged to offer Jumu‘ah if the conditions are met, in accordance with the general meaning of the texts of the Qur’an and Sunnah which indicate that it is an individual obligation upon the Muslims if the conditions stipulated in sharee‘ah are met.
Fataawa al-Lajnah ad-Daa’imah, 8/186
It is not stipulated that Jumu‘ah prayers should be held in a masjid (mosque) or jaami‘ (main mosque), according to the majority of Hanafi, Shaafa‘i and Hanbali fuqaha’; the Maalikis hold a different view.
Please see the answer to question no. 153872
Based on that, if there are three Muslim permanent residents in the city where you live, then you have to establish Jumu‘ah prayer, even if that is not in a mosque.
If there is no mosque in the city where you live or in a neighbouring town from which the call to prayer can be heard and you are able to go there, and there are no Muslims who could pray Jumu‘ah with you, then you are not obliged to pray Jumu‘ah; rather you should pray Zuhr when the time for it begins; you should not pray following the radio broadcast.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
I am on my own in Cyprus and I cannot find any Muslims with whom to pray; there is no mosque but I can hear the adhaan from one of the Arab countries on the radio, and I pray Jumu‘ah following the broadcast from one of the Arab countries. Is this prayer of mine regarded as prayer in congregation?
Undoubtedly Jumu‘ah prayer is obligatory upon the Muslims, but you should not pray following the radio broadcast; rather what is required of you is to look for Muslims who could establish Jumu‘ah prayer, and you have to put some effort into doing that. If you are able to find a congregation of Muslims in any mosque, you should pray Jumu‘ah with them, even if they are only two and you are the third one, because the correct opinion is that Jumu‘ah prayer may be held with three people, if they are settled and resident in a city and are not travellers. If they are residents and are settled, then you should all pray Jumu‘ah.
But if you are not able to find anyone, then you should pray Zuhr, with four rak‘ahs, after the sun has passed the zenith and the time for the prayer has begun; you should not pray Jumu‘ah unless there are two or more other people with you who are residents in the city. This is what has been stated by the scholars.
End quote from Fataawa Noor ‘ala ad-Darb, 13/182-184
He was also asked (may Allah have mercy on him):
We live in a town where there is no mosque; are we obliged to go to a mosque in the town that is 2 km away in order to pray Jumu‘ah? Is that required of someone who finds it difficult to reach the mosque in that town because the route is mountainous and rugged? What is the ruling on one who prays Zuhr instead in his house?
This matter is subject to further discussion. If the mosque is far away and they cannot hear the call to prayer and it is difficult for them to go to the mosque, then they are not obliged to do that, but they have to pray Zuhr in their places if they are not able to establish Jumu‘ah. If they are able to establish Jumu‘ah then they should establish it in their town, and they have no need to go to the other town. If they are three or more, then it is obligatory for them, according to the most correct scholarly opinion, to establish Jumu‘ah; one of them should deliver a khutbah (sermon) to the others and lead them in prayer; he may say in his khutbah whatever he can of words of exhortation and reminder to those who are present, and he should praise Allah and send blessings upon the Prophet (blessings and peace of Allah be upon him), and he should recite the Shahaadatayn (twin declaration of faith), and exhort and remind his brothers in whatever ways he can. Then he should sit down, then stand up again and give the second khutbah, reminding his brothers as he did in the first. Then he should lead them in praying two rak‘ahs in which he recites out loud, as is well known, and they do not have to go to the distant mosque.
But if it is possible to go there with other brothers and increase their numbers, and that does not entail any hardship for them, then going to join their brothers and pray with them is preferable. But they do not have to do that in the situation mentioned; they can establish Jumu‘ah in their own place and pray in their own place.
End quote from Fataawa Noor ‘ala ad-Darb, 13/138-140
See also the answer the question no. 45611
To sum up: no one should pray following the radio broadcast; rather if you can find someone with whom to pray Jumu‘ah in the place where you are staying, you should do so; if that is not possible, then pray Zuhr, as you do every day, and you do not have to pray Jumu‘ah in that case.
We ask Allah to help you to do that which He loves and which pleases Him.
And Allah knows best.