In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.

中文翻译：

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基于拉盖尔多项式数据非离散化的分数阶微分方程的一种新的数值处理

在这项研究工作中，我们讨论了具有分数阶的微分方程 (FODE) 的边值问题 (BVP) 的近似技术。我们通过应用拉盖尔多项式避免了数据离散化的方法，并为获得的数值解开发了一些操作类型的矩阵。通过应用运算矩阵，给定的问题被转换为一些代数方程，该方程在评估时给出了所需的数值结果。这些方程属于 Sylvester 类型，可以使用 matlab 求解。我们提供了一些测试示例以确保所考虑技术的正确性。