New Fractional Modelling, Analysis and Control of the Three Coupled Multiscale Non-Linear Buffering System.

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.