Affine Frequency Division Multiplexing (AFDM) is considered as a promising solution for next-generation wireless systems due to its satisfactory performance in high-mobility scenarios. By adjusting AFDM parameters to match the multi-path delay and Doppler shift, AFDM can achieve two-dimensional time-frequency diversity gain. However, under fractional delay-Doppler channels, AFDM encounters energy dispersion in the affine domain, which poses significant challenges for signal detection. This paper first investigates the AFDM system model under fractional delay-Doppler channels. To address the energy dispersion in the affine domain, a unitary transformation based approximate message passing (UAMP) algorithm is proposed. The algorithm performs unitary transformations and message passing in the time domain to avoid the energy dispersion issue. Additionally, we implemented block-wise processing to reduce computational complexity. Finally, the empirical extrinsic information transfer (E-EXIT) chart is used to evaluate iterative detection performance. Simulation results show that UAMP significantly outperforms GAMP under fractional delay-Doppler conditions.