Numerical scheme with convergence for a generalized time-fractional Telegraph-type equation
Numerical scheme with convergence for a generalized time-fractional Telegraph-type equation
复制标题
广义时间分数式电报型方程的收敛数值格式
DOI：
10.1002/num.22344
复制
发表时间：
2019
影响因子：
3.9
通讯作者：
Yufeng Xu
中科院分区：
文献类型：
--
作者：
K. Kumar;R.K. P;ey;S. Sharma;Yufeng Xu
本文设计并分析了用Agrawal最近提出的广义时间分数导数(GTFD)定义的广义时间分数阶电报类型方程(GTFTTE)的数值格式。GTFD包含标度函数和权重函数，对于特定的权重和标度函数的选择，简化为传统的卡普托导数。标度函数和权函数在描述真实物理系统的行为方面起着重要的作用，因此我们通过改变GTFTTE中的权函数和标度函数来研究GTFTTE的解行为。我们调查了GTFTTE在其中一些选择下的解决方案配置文件。我们还给出了GTFTTE数值格式的稳定性和收敛分析。我们考虑了两个测试实例来进行数值模拟。
In this work, we design and analyze a numerical scheme for solving the generalized time‐fractional Telegraph‐type equation (GTFTTE) which is defined using the generalized time fractional derivative (GTFD) proposed recently by Agrawal. The GTFD involves the scale and the weight functions, and reduces to the traditional Caputo derivative for a particular choice of the weight and the scale functions. The scale and the weight functions play an important role in describing the behavior of real‐life physical systems and thus we study the solution behavior of the GTFTTE by varying the weight and the scale functions in the GTFD. We investigate the solution profile of the GTFTTE under some of these choices. We also provide the stability and the convergence analysis of the proposed numerical scheme for the GTFTTE. We consider two test examples to perform numerical simulations.