In this work, a category of delay distributed-order time fractional fourth-order sub-diffusion equations is investigated. The Chebyshev cardinal polynomials (as a proper class of basis functions) are employed to make an appropriate methodology for these problems. To this end, some matrix relationships regarding the distributed-order fractional differentiation (in the Caputo kind) of these polynomials are extracted and applied in generating the desired approach. The provided method converts solving these problems into obtaining the solution of systems of algebraic equations. The reliability of the technique is evaluated by solving three examples.

中文翻译：

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延迟分布阶分数四阶子扩散方程的切比雪夫基数多项式

在这项工作中，研究了一类延迟分布阶时间分数四阶子扩散方程。Chebyshev 基数多项式（作为一类适当的基函数）用于为这些问题制定适当的方法。为此，提取了一些关于这些多项式的分布阶分数微分（Caputo 类型）的矩阵关系，并将其应用于生成所需的方法。所提供的方法将解决这些问题转化为获得代数方程组的解。通过解决三个例子来评估该技术的可靠性。