Doppler spread is a phenomenon caused by rapid changes in the channel response due to the movement of the transmitter/receiver through a multipath environment, which is also known as a doubly selective channel response. In doubly selective fading channel where the channel frequency response is regarded as rapidly time-varying, the inter carrier interference (ICI) occurs mainly because the traditional multicarrier transceivers are incapable to diagonalize the channel matrix. The proposed scenario is for an Orthogonal Chirp Division Multiplexing (OCDM) multicarrier system derived from Discrete Fractional Cosine Transform (DFrCT). The proposed DFrCT-OCDM multicarrier system is proofed to be less signal processing complexity and easier to implement, compared to the traditional Fast Fourier Transform (FFT). Simulation results reveal that the DFrCT provides superior performance reflected the significant improvement in the BitError Rate which reaches to 10 dB, better spectrum efficiency and better energy concentration properties than the conventional FFT. Finally, several equlizers are applied and they all show that the proposed DFrCT-OCDM over performs the other systems with all these equlizers.