In this paper, the multi-parameter time fractional radially symmetric anomalous diffusion model used in porous media with initial singularity is considered. Both the direct numerical solution problem and the multi-parameter identification inverse problem are studied. Given the singularity in the initial time, a stable numerical scheme on nonuniform grid mesh is derived by using the $L2-1_{\sigma }$ method. To conduct the multi-parameter inversion problem, a novel hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is proposed to combine the advantages of both the BWO algorithm and the CS algorithm, in order to improve the convergence speed and to achieve high-accuracy optimal results. Numerical examples are given to verify the efficiency and accuracy of the proposed numerical scheme and parameter inversion algorithm. Results show that the nonuniform grid $L2-1_{\sigma }$ scheme is efficient to deal with the time fractional radially symmetric anomalous diffusion problem with initial singularity, and the hybrid BWOCS algorithm has high precision and well convergence speed, compared with both the BWO and CS algorithms, which can be extended to other fractional inverse problems.

本文考虑了具有初始奇点的多孔介质中使用的多参数时间分数径向对称反常扩散模型。对直接数值求解问题和多参数辨识逆问题进行了研究。考虑到初始时刻的奇异性，利用以下公式导出了非均匀网格的稳定数值格式$L2-1_{\sigma }$方法。针对多参数反演问题，结合BWO算法和CS算法的优点，提出了一种新的混合黑寡妇优化和布谷鸟搜索(BWOCS)算法，以提高收敛速度并实现高收敛性。准确度最佳结果。数值算例验证了所提出的数值方案和参数反演算法的效率和准确性。结果表明，非均匀网格$L2-1_{\sigma }$该方案能够有效地处理具有初始奇点的时间分数式径向对称反常扩散问题，并且与BWO和CS算法相比，混合BWOCS算法具有较高的精度和良好的收敛速度，可推广到其他分数反问题。