In this paper, it is shown that the mathematical description of the bulk fluid flow and that of content impurity spread, which uses temporal Caputo or temporal Riemann–Liouville fractional order partial derivatives, having integral representation on a finite interval, in the case of a horizontal unconfined aquifer is non-objective. The basic idea is that different observers using this type of description obtain different results which cannot be reconciled, in other words, transformed into each other using only formulas that link the numbers representing a moment in time for two different choices from the origin of time measurement. This is not an academic curiosity; it is rather a problem to find which one of the obtained results is correct.

Our goal is the oscillation susceptibility analysis in the framework of a nonlinear mathematical model in the so-called ADMIRE or Aero Data Model in a Research Environment. First, we analyze the oscillation susceptibility along the path of the longitudinal flight equilibriums when the flight control system (FCS) is decoupled. After that, a similar analysis is undertaken in the case when the FCS is coupled. For decoupled FCS, it is shown that on the path of the longitudinal flight equilibriums there exists a saddle-node where stability is lost and fold bifurcation occurs. Maneuvers are simulated showing the effect of an instantaneous change of the elevator angle, and the evolution of the unstable equilibriums (due to the maneuvers) to the corresponding exponentially stable equilibriums. It is shown numerically that at the saddle-node oscillations occur when the elevator angle is less than the critical value and the start is from the saddle-node. More precisely, it is shown that if the plane state parameters coincide with the saddle-node coordinates and the elevator angle is changed instantaneously from the critical value to a value which is less than this value, then two of the state parameters $\left(\alpha ,q\right)$ begin to oscillate with the same period and the third parameter $\left(\theta \right)$ increases, tending to infinity. Thus, the orbit of the system evolves spiraling. It is shown also, that if the elevator angle is reset, the plane returns to a stable equilibrium. Therefore, a soft or no catastrophic stability loss takes place. When the FCS is coupled, the plane for every value of the amplification factor has a unique equilibrium which is exponentially stable and attracts all the equilibriums which exist in decoupled case. In this case, there are no bifurcation points on the equilibrium path. The dependence of the equilibrium and of the relaxation period on the amplification factor value is found numerically. Finally, it is concluded that when the FCS is decoupled, then along the path of the longitudinal equilibriums oscillations can occur, but when the FCS is coupled and the pilot can modify (instantaneously) only the amplifier factor value, then the vehicle, defined by the considered numerical data, is not anymore susceptible to oscillation.

This study presents sufficient conditions for the stability or instability of the static liquid bridge appearing in crystal growth from the melt of micro-fibers, thin plates, and hollow micro-tubes of predetermined sizes using the pulling-down method. The case in which the contact angle and the growth angle verify the inequality ${\alpha }_c>\pi /2-{\alpha }_g$ is considered. Experimentally, only stable static liquid bridges can be created; unstable static liquid bridges exist just in theory, because in reality they collapse. The results of this study are significant for shaped crystal growth from melted materials, with given macroscopic dimensions, and using specific equipment. This is because the obtained inequalities represent limits for what can and cannot be achieved experimentally.

The well posedness of the perturbation propagation problem and the Lyapunov stability of a spatially developing constant 2D gas flow is analyzed in a particular infinite dimensional phase space. The elements of the phase space are continuously differentiable functions, the algebraic operations are usual and the topology is that generated by the uniform convergence. The well posedness of the propagation problem as well the Lyapunov stability with respect to the instantaneous and with respect to source produced permanent time harmonic perturbations is investigated. Some of the obtained results are completely different from those reported in the literature.

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].