This work considers the subdiffusion motion of information carrying molecules inside a molecular communication (MC) channel. Additionally, an evanescence process is taken into account, which leads to the degradation of molecules prior to their hitting to the receiver's boundary. The closed-form expressions of the arrival probability and the first-passage-time-density (FPTD) are obtained. Furthermore, the performance of MC was investigated by using the concentration-based modulation technique. The probability of detection is presented for different parameters of a reaction rate. The performance results were validated by the Monte-Carlo simulation.