Orthogonal time frequency space (OTFS) modulation has been proposed to achieve outstanding performances over delay-Doppler channels in comparison with orthogonal frequency division multiplexing (OFDM) systems. Particularly, transmitter and receiver structures of OTFS are same as those of asymmetric OFDM (A-OFDM) waveforms, and OTFS is simplified as A-OFDM over static multipath channels. In this letter, we propose an integrated waveform framework based on weighted-type fractional Fourier transform (WFRFT) with two-dimensional adjustable parameters and strong scalability, called as WFRFT-OTFS, which can be reduced to OTFS, A-OFDM, hybrid carrier (HC), OFDM and other waveforms. Basically, theoretical BER expressions of integrated WFRFT-OTFS framework over multipath channels with zero forcing (ZF) and minimum mean square error (MMSE) receivers are derived through fusing different waveform components and verified by simulation results.