All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Determining the times of prayer, issued by the official authorities in the Islamic countries, was conducted through the inspection and survey of specialized committees, which stationed in certain locations and observed the times of prayer over the year utilizing astronomical calculations. However, in case there is a difference between these times and those offered by the apps, then a Muslim must follow the times issued by the official authorities in his country and he is cleared from liability and his prayer is valid Insh`Allah. This is because the person who doesn`t know the times of prayer and their indications must imitate the scholar who relies on physical evidence in this regard or the Mujtahid (a person accepted as an original authority in Islamic law) who relies on conjectural evidence.
For more details, kindly check the book entitled {Bushra Al-Kareem, P.178}.
As for the modern applications that calculate the times of prayer, they are based on accurate calculations connected to equations founded on astronomical calculations. These apps take different factors into consideration: person`s location, latitude, temperature, humidity, the angle of refraction and other factors that affect the accuracy of the prayer times. Moreover, there could be some differences between the times of prayer according to these apps and the times of Azan applied in the country depending on taking all these factors or some of them into consideration.
In conclusion, the time of Azan must be relied on in determining the time of prayer as well as the beginning and end of fasting. This is in order to preserve the unity of the Muslim nation, spare the people getting confude in their acts of worship or causing them to doubt their religion. However, if a Muslim lives in a remote area and can`t hear the Azan, then, in this case, there is no sin in relying on these applications. And Allah the Almighty knows best.