Fractional differential equations sufficiently depict the nature in view of the symmetry properties, which portray physical and biological models. In this paper, we present a proficient collocation method based on cubic trigonometric B-Splines (CuTBSs) for time-fractional diffusion equations (TFDEs). The methodology involves discretization of the Caputo time-fractional derivatives using the typical finite difference scheme with space derivatives approximated using CuTBSs. A stability analysis is performed to establish that the errors do not magnify. A convergence analysis is also performed The numerical solution is obtained as a piecewise sufficiently smooth continuous curve, so that the solution can be approximated at any point in the given domain. Numerical tests are efficiently performed to ensure the correctness and viability of the scheme, and the results contrast with those of some current numerical procedures. The comparison uncovers that the proposed scheme is very precise and successful.

考虑到对称性，分数阶微分方程足以描述自然，它描述了物理和生物学模型。在本文中，我们提出了一种基于三次三角B样条（CuTBS）的时间-分数扩散方程（TFDE）的高效配置方法。该方法包括使用典型的有限差分方案对Caputo时间分数导数进行离散化，并使用CuTBS近似空间导数。执行稳定性分析以确保误差不会放大。还进行了收敛性分析。数值解以分段足够平滑的连续曲线的形式获得，因此该解可以在给定域中的任何点处近似。有效地进行了数值测试，以确保该方案的正确性和可行性，结果与某些当前数值程序的结果形成对比。通过比较发现，该方案非常精确且成功。