In this paper, by combining fractional calculus and sliding mode control theory, a new fractional order adaptive terminal sliding mode controller is proposed for the maximum power point tracking in a solar cell. To find the maximum power point, the incremental conductance method has been used. First, a fractional order terminal sliding mode controller is designed in which the control law depends on knowing the upper bound of uncertainty in the system, but in practical application it is difficult or in some cases impossible to calculate this upper limit. In this paper, an adaptive law is given for online calculating of this parameter. The stability proof of the sliding surface, as well as the proof of finite time convergence of closed-loop system, are investigated using the Lyapunov theory. Finally, the performance of the proposed controller is evaluated both in normal and partial shading conditions. For a better comparison of the proposed controller, the performance of this controller is compared in the presence of load variations and the variations of system parameters with the conventional (integer order) terminal sliding mode control.