This study contains numerical schemes namely Linear scheme, Quadratic scheme, and Quadratic–linear scheme to solve a fractional integro-differential equation using the Atangana–Baleanu derivative defined in Caputo sense. The error bounds of the schemes are obtained. We discuss four test examples to perform the numerical simulations, and the obtained numerical results ensure that the presented schemes work well and the obtained approximate solution agrees with the analytical solution. The convergence order and maximum absolute errors of the schemes are calculated and their comparative performances are discussed.

中文翻译：

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求解卡普托意义定义的 Atangana-Baleanu 分数阶积分微分方程的三种数值方案的比较研究

本研究包含数值方案，即线性方案、二次方案和二次-线性方案，以使用 Caputo 意义上定义的 Atangana-Baleanu 导数求解分数阶积分-微分方程。获得了方案的误差界限。我们讨论了四个测试实例来进行数值模拟，获得的数值结果确保所提出的方案工作良好，并且获得的近似解与解析解一致。计算了这些方案的收敛阶数和最大绝对误差，并讨论了它们的比较性能。