In this article, a semi-analytical technique called optimal homotopy asymptotic method (OHAM) is presented for numerical solutions of fractional-order integro-differential equations. The fractional-order derivatives are calculated using Caputo sense. The efficiency and reliability of proposed method is verified with multiple examples. Results of proposed method are compared with trigonometric transform method, standard least square method and perturbed least square method. The obtained results reveal that the proposed method is rapidly convergent, more reliable and easy to implement.

中文翻译：

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最优同伦渐近方法求解分数阶积分微分方程

本文针对分数阶积分微分方程的数值解提出了一种称为最佳同伦渐近方法（OHAM）的半解析技术。分数阶导数是使用Caputo感计算的。通过多个实例验证了所提方法的有效性和可靠性。将该方法的结果与三角变换法，标准最小二乘法和扰动最小二乘法相比较。所得结果表明，该方法快速收敛，更可靠，易于实现。