This paper focuses on a numerical study of the general time-space variable-order fractional nonlinear problem of thermoelasticity in one dimension using the weighted average nonstandard finite difference (WANSFD). By replacing the second order space derivative with a Riesz fractional variable-order derivative and the time derivative by Caputo fractional variable-order operator in the standard system which arises in thermoelasticity, we obtain this general system. Using a kind of John von Neumann technique, we study the stability of the designed schemes. Also, the truncation error of the introduced schemes is studied. Our numerical treatment is shown graphically. These results expose that WANSFD approach is suitable and effective for solving the proposed system; moreover, it is easy to implement.

本文着重使用加权平均非标准有限差分（WANSFD）对一维热弹性的一般时空变阶分数阶非线性问题进行数值研究。通过在热弹性中产生的标准系统中，用Caputo分数阶变量算子将Riesz分数阶变量微分和时间导数替换为Riesz分数阶空间微分，可以得到该通用系统。使用一种约翰·冯·诺伊曼技术，我们研究了设计方案的稳定性。此外，研究了引入方案的截断误差。我们的数值处理以图形方式显示。这些结果表明，WANSFD方法适合于解决所提出的系统；此外，它易于实现。