Using jQuery you could change the start time and end time of the appointment, which means the time slot for the appointment will be changed also.
I believe the following help articles will be also useful to implement the scenario in question:
RadSchduler: Methods and Properties
and RadSchduler Appointment: Methods and Properties
You should keep in mind that the updateAppointment
client-side method of RadScheduler should be called after the changes made for the current appointment.
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