This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and homotopy perturbation method. Moreover, this paper proves the convergence analysis of the solution based on the present methods. Numerical evidences are illustrated in support of the theoretical analysis.

中文翻译：

---

时间分数阶偏积分微分方程解的Adomian分解和同伦摄动法

本文讨论求解时间分数式偏积分微分方程的两种不同方法。这里的分数导数是在 Caputo 意义上定义的。使用Adomian分解方法和同伦微扰方法解决模型问题。此外，本文还证明了基于现有方法的解的收敛性分析。数字证据被说明以支持理论分析。