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Abstract：
This paper demonstrates, a numerical method to solve the one and two dimensional Burgers\' equation involving time fractional Atangana-Baleanu Caputo ( ABC ) derivative with a non-singular kernel. The numerical stratagem consists of a quadrature rule for time fractional ( ABC ) derivative along with Haar wavelet (HW) approximations of one and two dimensional problems. The key feature of the scheme is to reduce fractional problems to the set of linear equations via collocation procedure. Solving the system gives the approximate solution of the given problem. To verify the effectiveness of the developed method five numerical examples are considered. Besides this, the obtained simulations are compared with some published work and identified that proposed technique is better. Moreover, computationally the convergence rate in spatiotemporal directions is presented which shows order two convergence. The stability of the proposed scheme is also described via Lax-Richtmyer criterion. From simulations it is obvious that the scheme is quite useful for the time fractional problems.
摘要：
本文论证了,一种数值方法，用于求解涉及具有非奇异核的时间分数Atangana-BaleanuCaputo（ABC）导数的一维和二维Burgers方程。数值策略由时间分数（ABC）导数的正交规则以及一维和二维问题的Haar小波（HW）近似组成。该方案的关键特征是通过搭配过程将分数问题简化为线性方程组。求解该系统给出了给定问题的近似解。为了验证所开发方法的有效性，考虑了五个数值示例。除此之外,将获得的模拟与一些已发表的工作进行比较，并确定提出的技术更好。此外，在计算上给出了时空方向的收敛速度，显示了二阶收敛。还通过Lax-Richtmyer准则描述了所提出方案的稳定性。从仿真中可以明显看出，该方案对于时间分数问题非常有用。
