A numerical treatment to a system of Caputo fractional order differential- algebraic equations (SFDAEs) is presented throughout this article. The suggested method based upon the shifted Chebyshev pesedu- spectral method (SCPSM). The shifted Chebyshev polynomials (SCPs) are handled to reduce the SFDAEs into the solution of linear/ nonlinear systems of algebraic equations. By using some tested applications, the effectiveness and the accuracy of the suggested approach are demonstrated graphically. Also numerical comparisons between the proposed technique with other numerical methods in the existing literature are held. The numerical results show that the proposed technique is computationally efficient, accurate and easy to implement.

本文通篇介绍了Caputo分数阶微分代数方程组（SFDAE）的数值处理。建议的方法基于偏移的Chebyshev谱图方法（SCPSM）。处理移位的Chebyshev多项式（SCP）可将SFDAE简化为代数方程的线性/非线性系统的解。通过使用一些经过测试的应用程序，以图形方式展示了所建议方法的有效性和准确性。还对所提出的技术与现有文献中的其他数值方法进行了数值比较。数值结果表明，该技术具有计算效率高，准确度高，易于实现的特点。