Build an hour booking calendar with events and hide not available hours

For a new project, I have to built an hour booking calendar for doctors. I'm looking for a plugin (js / vanilla / jquery / vuetify / react) that can respond to the following needs:

• have a weekly view of the current week (with a week pagination: w+1 / w+2 etc)
• display only available hours of the doctor (hide taken appointent / hourly)
• trigger an event from an hour pick

Here is an exemple of exactly what I would like to achieve

What is the best plugin that can help me with this? Also, doctors already have their own calendars. I will have to synchronise their calendar with mine, what is the best way to achieve this? How can I store all theses informations?

Don't hesitate to ask me questions

Thanks in advance

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