Partohaghighi Mohammad, Yusuf Abdullahi, Bayram Mustafa
Department of Mathematics, Clarkson University, Potsdam, NY 13699 USA.
Department of Computer Engineering, Biruni University, Istanbul, Turkey.
Int J Appl Comput Math. 2022;8(2):86. doi: 10.1007/s40819-022-01290-9. Epub 2022 Mar 27.
This study aims to investigate the complicated dynamical buffering system using fractional operators which is not been investigated yet. We consider a new fractional mathematical model in the frame of fractional-order differential equations. In the proposed fractional-order model, we apply the Caputo-Fabrizio fractional operator with an exponential kernel. Then to solve the derived system of fractional equations, we suggest a quadratic numerical technique and prove its stability and convergence. Also, accurate control for the proposed system is considered. Behaviors of the approximate solutions for the considered model are provided by choosing different values of fractional orders along with integer order. Each figure manifests and compares the numerical solutions under selected orders. Figures, show how the results can be affected by changing the fractional orders.
本研究旨在利用尚未被研究的分数阶算子来研究复杂的动态缓冲系统。我们在分数阶微分方程的框架内考虑一个新的分数阶数学模型。在所提出的分数阶模型中，我们应用具有指数核的卡普托 - 法布里齐奥分数阶算子。然后，为了解所导出的分数阶方程组，我们提出一种二次数值技术并证明其稳定性和收敛性。此外，还考虑了对所提出系统的精确控制。通过选择不同的分数阶值以及整数阶值，给出了所考虑模型的近似解的行为。每个图展示并比较了所选阶数下的数值解。这些图展示了改变分数阶如何影响结果。
