Is there any concept of banking in ISLAM?

Yes, in islam banking exists but it should the interest fee (Ribah free) and it had many closed substitutes of  commercial banking tools. Like

Modaribah,

Musharikah

Ijarah,

The banking is a new terminology raised on the new era of building the economies of countries. However, the Islamic countries (those who are the majority of its population are Muslims) when they start building their economies from the end of 19th century and the beginning of the 20th century they didn’t implement their own module of economics because most of these countries were suffering at that time from the nescience and Illiteracy and the education efficiency was at the very low level. Also, at that era, Britain and France were controlling most of these countries and having the lead and the power of applying strategies and regulations.

Accordingly, the concept of banking has been transferred from the western government by default (or may be by force) and not all of these modules were compatible with the Shariah of Islam.

After decades, the economies of these countries become more prudent enough to develop their own modules and the awareness of Shariah becomes in place.

Going back to your question about the concept of banking in Islam. The Islam has generated his regulations from the Holy Quran (i.e. the holy book of God) and Sunnah (i.e. Prophet Muhammad’s directions and daily events). Then, the Islamic scholars (U‘llamaa) have extracted the purposes of the Shariah law based on their conscientiousness and judgement and their effort and guidance become the base of understanding the doctrine of Islam.

Therefore, the concept of Banking was not part, initially, of the Shariah regulations until the practices of the financial transactions has become an essential part of the economies and  U’llamah start to highlight some concerns on the current practices and how it is not compliant with the Shariah law.

By the way, the number of those who are interesting in the Islamic finance studies are increasing every day and a lot of persons become qualified on the Islamic Economics. They are playing a role to implement the current regulations on their countries to let all transactions compatible with the Shariah law.