Abstract A new finite difference collocation algorithm has been introduced with the help of Fibonacci polynomial and then applied to one super and two sub-diffusion problems having an exact solution. It has also been shown that numerical error obtained with the investigated method is more accurate than previously existing methods. Fractional order reaction advection sub-diffusion equation containing Caputo and Riemann–Liouville fractional derivatives has been solved and the effects due to change in various parameters presented in the considered model with the graphical representation have been discussed.

中文翻译：

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二维分数阶反应平流子扩散方程的有限差分斐波那契配置法数值解

摘要 借助斐波那契多项式引入了一种新的有限差分搭配算法，并将其应用于具有精确解的一超二子扩散问题。还表明，使用所研究的方法获得的数值误差比以前存在的方法更准确。已经求解了包含 Caputo 和 Riemann-Liouville 分数阶导数的分数阶反应平流子扩散方程，并讨论了由于在所考虑的模型中呈现的各种参数的变化以及图形表示的影响。