The fractional integrals involving a number of special functions and polynomials have significant importance and applications in diverse areas of science; for example, statistics, applied mathematics, physics, and engineering. In this paper, we aim to introduce a slightly modified matrix of Riemann–Liouville fractional integrals and investigate this matrix of Riemann–Liouville fractional integrals associated with products of certain elementary functions and generalized Bessel matrix polynomials. We also consider this matrix of Riemann–Liouville fractional integrals with a matrix version of the Jacobi polynomials. Furthermore, we point out that a number of Riemann–Liouville fractional integrals associated with a variety of functions and polynomials can be presented, which are presented as problems for further investigations.

中文翻译：

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与涉及广义贝塞尔矩阵多项式的函数相关的某些矩阵黎曼–利维尔分数阶积分

涉及许多特殊函数和多项式的分数积分在科学的各个领域具有重要的意义和应用。例如统计，应用数学，物理学和工程学。在本文中，我们旨在介绍经过稍微修改的Riemann-Liouville分式积分矩阵，并研究与某些基本函数乘积和广义Bessel矩阵多项式的乘积相关联的Riemann-Liouville分式积分矩阵。我们还考虑了Riemann-Liouville分数积分的矩阵和Jacobi多项式的矩阵形式。此外，我们指出，可以提出与各种函数和多项式相关的许多黎曼-利维尔分数积分，这些问题作为进一步研究的问题。