The paper deals with the issues of parallel computations’ organization while solving three-dimensional space-fractional diffusion equation with the \(\psi \)-Caputo derivatives using finite difference schemes. For an implicit scheme and locally one-dimensional splitting scheme, we present parallel algorithms for distributed memory systems that use one-dimensional block and red–black data partitioning. To reduce the order of algorithms’ computational complexity, we use an approach based on the expansion of integral operator’s kernel into series. We present the theoretical estimates of parallel algorithms’ performance and the results of computational experiments conducted on a testing problem that has an analytical solution for the case of the Caputo–Katugampola derivative. The results of the experiments show close-to-linear parallelization efficiency of one-dimensional splitting scheme with block partitioning and inefficiency of red–black partitioning in this case. For the implicit scheme, the scalability of parallel algorithms is weak and the use of red–black partitioning is more efficient than the use of block partitioning when running on a small number of computational resources.

本文在用\（\ psi \）解决三维空间分数维扩散方程的同时，解决了并行计算的组织问题。-Caputo导数使用有限差分方案。对于隐式方案和局部一维拆分方案，我们提出了使用一维块和红黑数据分区的分布式存储系统的并行算法。为了降低算法的计算复杂性，我们使用了一种基于将积分运算符的核扩展为级数的方法。我们介绍了并行算法性能的理论估计以及对一个测试问题进行的计算实验的结果，该问题对Caputo–Katugampola导数的情况具有解析解。实验结果表明，在这种情况下，具有块分割的一维分割方案接近线性并行化效率，而红黑分割效率低下。对于隐式方案，