New Stabilization Results for the One‐Dimensional Fractional‐Time Glycolysis Reaction‐Diffusion System Through Neumann Boundary Feedback Controls

ABSTRACT

Stabilization of the linearized time fractional reaction‐diffusion system in one‐dimensional modeling glycolysis (LFRDG) has been rigorously studied. First, the nonlinear fractional reaction‐diffusion (NLFRDG) system is linearized around a steady‐state. Then, using semigroup theory on Banach spaces, we demonstrated that the LFRDG system with homogeneous Neumann boundary conditions admits a unique global solution. Furthermore, we have proven that such a solution is Mittag‐Leffler (ML) stable. In the second part of this work, using a backstepping approach, we proved that there exists Neumann feedback boundary controls such that the LFRDG system is ML stable. In fact, the results obtained here are new in the context of the stabilization for the LFRDG models by Neumann‐type boundary controls through the backstepping method. Finally, some numerical examples are presented to illustrate the theoretical results.