Reliable and energy-efficient wireless data transmission remains a major challenge in resource-constrained wireless neural recording tasks, where data compression is generally adopted to relax the burdens on the wireless data link. Recently, Compressed Sensing (CS) theory has successfully demonstrated its potential in neural recording application. The main limitation of CS, however, is that the neural signals have no good sparse representation with commonly used dictionaries and learning a reliable dictionary is often data dependent and computationally demanding. In this paper, a novel CS approach for implantable neural recording is proposed. The main contributions are: 1) The co-sparse analysis model is adopted to enforce co-sparsity of the neural signals, therefore overcoming the drawbacks of conventional synthesis model and enhancing the reconstruction performance. 2) A multi-fractional-order difference matrix is constructed as the analysis dictionary, thus avoiding the dictionary learning procedure and reducing the need for previously acquired data and computational resources. 3) By exploiting the statistical priors of the analysis coefficients, a weighted analysis $\ell_1$-minimization (WALM) algorithm is proposed to reconstruct the neural signals. Experimental results on Leicester neural signal database reveal that the proposed approach outperforms the state-of-the-art CS-based methods. On the challenging high compression ratio task, the proposed approach still achieves high reconstruction performance and spike classification accuracy.