Saad K M, Khader M M, Gómez-Aguilar J F, Baleanu Dumitru
Department of Mathematics, Faculty of Arts and Sciences, Najran University, P.O. Box 1988, Najran City, Saudi Arabia.
Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 1440, Riyadh, Saudi Arabia.
Chaos. 2019 Feb;29(2):023116. doi: 10.1063/1.5086771.
The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher's equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
本文的主要目的是研究一种通过阿坦加纳-巴莱努分数阶导数求解生物分数模型的精确数值方法。我们将注意力集中在线性和非线性费舍尔方程上。我们使用基于切比雪夫近似的谱配置方法。该方法利用切比雪夫多项式的性质将非线性方程简化为常微分方程组，然后使用有限差分法求解。这是首次将该方法用于求解阿坦加纳-巴莱努意义下的非线性方程。我们通过计算绝对误差和残差误差函数来展示所提方法的有效性和准确性。结果表明，给定的过程是研究具有局部和非局部奇异核的非线性方程解的一种简便且有效的工具。
