On the fractional-order glucose-insulin interaction

Abstract

<abstract><p>We consider a fractional-order model of glucose and insulin interaction based on the intra-venous glucose tolerance test (IVGTT). We show the existence of the model's solution, uniqueness, non-negativity, and boundadness. In addition, for the proposed fractional-order model, we establish sufficient conditions for stability or instability. Some conditions for bifurcation in the proposed model are presented using bifurcation theory. Further, in the case of first order the model is discretized by applying the forward Euler scheme. We investigate how small the time step size must be chosen to guarantee that the steady state solution is an attractive fixed point of the discretized model. Numerical simulations that we provided support the analytical results.</p></abstract>

Analysis and Applications of the Chaotic Hyperbolic Memristor Model with Fractional Order Derivative

“…As we embark on the next phase of research, the focus will shift towards the deployment and electronic integration of this innovative system, promising new av-enues for exploration in the field of nonlinear dynamical systems. This work lays the groundwork for future research, highlighting the potential for further advancements in the domain of fractional-order chaotic systems and their practical applications.We proposed to compare numerical solutions with other ways [5,33,35] and use this method to solve novel fractional issues [7,9,11,12,14,21,23,25,31,32,34]…”

“…The Lyapunov exponents are calculated for system (5) with integer and fractional order ζ = 1 and ζ = 0.99 respectively. The values at integer order ζ = 1 are 0.0796, 0, −0.838 and at ζ = 0.99 the values are 0.0520, −0.05266, −0.92940.…”