Abstract For a class of tempered fractional integro-differential equation of the Caputo type, a comparative study of three numerical schemes is presented in this paper. The schemes discussed are Linear, Quadratic and Quadratic-Linear schemes. Four numerical examples are considered to discuss error estimate and convergence order of the numerical schemes for different values of step-size h and the parameter λ. Numerical results are presented through tables and figures which validate the analytical solution of the test examples. Further, the comparative performances of the presented numerical schemes are discussed.

中文翻译：

---

一类调和分数阶积分微分方程的数值格式

摘要 本文针对一类Caputo型淬火分数阶积分微分方程，对三种数值格式进行了比较研究。讨论的方案是线性、二次和二次线性方案。考虑四个数值例子来讨论不同步长 h 和参数 λ 值的数值方案的误差估计和收敛顺序。数值结果通过表格和图形呈现，验证了测试实例的解析解。此外，还讨论了所提出的数值方案的比较性能。