In this paper, we investigate the solution of multi-term time-space fractional partial delay differential-algebraic equations (MTS-FPDDAEs) with Dirichlet boundary conditions defined on a finite domain. We use Laplace transform method to give the solutions of multi-term time fractional delay differential-algebraic equations (MTS-FDDAEs). Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the MTS-FPDDAEs into the MTS-FDDAEs. By applying our obtained solutions to the resulting MTS-FDDAEs, the desired analytical solutions of the MTS-FPDDAEs are obtained. Finally, we give the solutions of some special cases.

在本文中，我们研究了在有限域上定义 Dirichlet 边界条件的多项时空分数偏延迟微分代数方程 (MTS-FPDDAE) 的解。我们使用拉普拉斯变换方法给出了多项时间分数延迟微分代数方程（MTS-FDDAEs）的解。然后，利用分数拉普拉斯算子的谱表示技术将MTS-FPDDAEs转换为MTS-FDDAEs。通过将我们获得的解决方案应用于生成的 MTS-FDDAE，获得所需的 MTS-FPDDAE 分析解决方案。最后，我们给出了一些特殊情况的解决方案。