In this study, Bernstein approximation method has been applied along with Riemann–Liouville fractional integral operator to solve both the second and the first kind of fractional Volterra integral equations (2nd FVIEs and 1st FVIEs respectively). In order to show the applicability and efficiency of the proposed technique, some convergence analysis has been provided. Illustrative numerical experiments with comparison are included to indicate the validity and practicability of the method. All of the numerical calculation in this research has been done on a personal computer implementing some programs written in MATLAB.

中文翻译：

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分数阶Volterra积分方程的Bernstein逼近数值分析

在这项研究中，Bernstein逼近方法与Riemann-Liouville分数积分算子一起被应用来求解第二和第一类分数阶Volterra积分方程（分别是第二FVIE和第一FVIE）。为了显示所提出技术的适用性和效率，已经提供了一些收敛性分析。包括说明性的数值实验和比较，以表明该方法的有效性和实用性。这项研究中的所有数值计算都是在个人计算机上完成的，该计算机执行了一些用MATLAB编写的程序。