Corrosion-degradation models may be applied to systems where current degradation state depends on past exposures and cyclic environment forcing. Fractional derivative models are fit to such cases as they maintain memory. However, a memory-filled model alone cannot be considered as a reliability certificate. The analysis of a service-oriented model also requires specification of whether any bounded uncertainty in electrolyte chemistry, temperature, wetness history, oxygen access or measurement noise is also bounded in the chosen damage variables. The core of the problem is to verify whether the generalized proportional Caputo system can give a Lyapunov certificate that would link fading memory, bounded environmental disturbances and corrosion-state boundedness. In this analysis, the comparison theorem for non-autonomous nonlinear fractional order systems with generalized Caputo derivatives is formulated and used to analyze a two-state example of a numerical corrosion process. The model is constructed based on the stated equations with $\alpha\in\{0.55,0.70,0.85\}$, $\rho\in\{0.70,0.85,0.90,0.95,1.00\}$, $x(0)=(0.52,0.52)^\top$, $g(t)=-1+0.25\sin(0.3t)$, $\delta\in\{0,0.01,0.03,0.05\}$, $T=40$ and $h=0.02$. The results imply that the proportional parameter $\rho$ serves as a stability-related memory parameter and not just as a tuning one. With $\delta=0.03$, for example, the case of $(\alpha,\rho)=(0.70,0.70)$ attains the threshold of $\lVert x \rVert<0.05$ at approximately $t=13.6$, while the case with the same $\alpha$ and $\rho=0.95$ does not attain the threshold even at $T=40$. As $\rho$ varies from $0.70$ to $0.95$ with the same disturbance amplitude, robust certificate radii grow from $0.200$ to $1.200$. Another nonlinear saturation kinetics evaluation gives a radius of about $0.084$ for $r=0.75$, $a=0.40$, and $\delta = 0.03$. It is found from the investigation that generalized proportional Caputo derivatives have applications in evaluating corrosion behavior only when memory parameter, disturbance supply, and Lyapunov constants are mentioned together.

corrosion degradation,generalized proportional Caputo derivative,fractional stability,Lyapunov certificate,practical boundedness,disturbed materials models