The main purpose of this work is to study the numerical solution of a time fractional partial integro-differential equation of Volterra type, where the time derivative is defined in Caputo sense. Our method is a combination of the classical L1 scheme for temporal derivative, the general second order central difference approximation for spatial derivative and the repeated quadrature rule for integral part. The error analysis is carried out and it is shown that the approximate solution converges to the exact solution. Several examples are given in support of the theoretical findings. In addition, we have shown that the order of convergence is more high on any subdomain away from the origin compared to the entire domain.

这项工作的主要目的是研究 Volterra 类型的时间分数式偏积分微分方程的数值解，其中时间导数在 Caputo 意义上定义。我们的方法是时间导数的经典 L1 方案、空间导数的一般二阶中心差分近似和积分部分的重复正交规则的组合。进行误差分析，结果表明近似解收敛于精确解。给出了几个例子来支持理论发现。此外，我们已经表明，与整个域相比，远离原点的任何子域的收敛顺序都更高。