The main purpose of this work is to investigate an initial boundary value problem related to a suitable class of variable order fractional integro‐partial differential equations with a weakly singular kernel. To discretize the problem in the time direction, a finite difference method will be used. Then, the Sinc‐collocation approach combined with the double exponential transformation is employed to solve the problem in each time level. The proposed numerical algorithm is completely described and the convergence analysis of the numerical solution is presented. Finally, some illustrative examples are given to demonstrate the pertinent features of the proposed algorithm.

中文翻译：

---

一种有效的数值方法，用于求解一类分数阶积分-偏微分方程

这项工作的主要目的是研究与一类具有弱奇异核的变量阶分数阶积分-偏微分方程有关的初始边值问题。为了在时间方向上离散化问题，将使用有限差分法。然后，采用Sinc-colocation方法结合双指数变换来解决每个时间级别的问题。完整描述了所提出的数值算法，并给出了数值解的收敛性分析。最后，给出一些说明性的例子来说明所提出算法的相关特征。