This work addresses some robust control strategies for controlling the tip position tracking of a flexible two-link robotic arm manipulator with the consideration that the system is having very less friction and less mechanical vibration at the joints. The flexible two-link flexible manipulator is modelled using Euler-Lagrangian mechanics. Further, a fractional-order modelling is also done for the same system. The parameters of the system are taken from a real-time system. The sliding mode control strategy which is one of the robust control techniques can be made more robust using adaptive sliding mode and fractional-order adaptive sliding mode. The use of an adaptive sliding mode makes the tuning of the control parameters easier with a better response. The simulation results reveal that the adaptive sliding mode strategy is more robust in terms of changes in the initial conditions as well as disturbances to the system.