In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap(.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples.

中文翻译：

---

混合偏导项的广义运算矩阵在多阶分数式偏微分方程中的应用

在本文中，设计了一种基于运算矩阵与正交移位勒让德多项式 (OSLP) 相结合的计算方法，以数值求解由混合偏导项组成的分数阶多阶偏微分方程。我们的计算方法能够将分数问题简化为 Sylvester 类型矩阵方程系统，该系统可以使用MATLAB内置函数lyap (.)求解。该解近似为 OSLP 的基向量。通过各种测试示例来检查效率和数值稳定性。