Stability analysis of Caputo fractional-order nonlinear systems revisited

In this paper stability analysis of fractional-order nonlinear systems is studied. An extension of Lyapunov direct method for fractional-order systems using Bihari’s and Bellman–Gronwall’s inequality and a proof of comparison theorem for fractional-order systems are proposed.     

Transverse susceptibility as the low-frequency limit of ferromagnetic resonance

A new theory of transverse susceptibility (TS) based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the traditional TS experiment is, in fact, the zero-frequency limit of the ferromagnetic resonance (FMR). The importance of these results resides in the generality of the approach which allows one to find the TS for virtually any magnetic system if an expression for the magnetic free-energy density is known. Moreover, the effect of the frequency of excitatory AC field on the TS experiments and the effect of energy dissipation through the imaginary part of TS emerge coherently from the new TS model.     

A new fractional derivative involving the normalized sinc function without singular kernel

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.     

LMI-based stabilization of a class of fractional-order chaotic systems

Based on the theory of stabilization of fractional-order LTI interval systems, a simple controller for stabilization of a class of fractional-order chaotic systems is proposed in this paper. We consider the structure of the chaotic systems as fractional-order LTI interval systems due to the limited amplitude of chaotic trajectories. We introduce a simple feedback controller for the interval system and then, based on a recently established theorem for stabilization of interval systems, we reach to a linear matrix inequality (LMI) problem. Solving the LMI yields an appropriate decoupling feedback control law which suffices to bring the chaotic trajectories to the origin. Several illustrative examples are given which show the effectiveness of the method.     

Fractional Nambu Mechanics

The fractional generalization of Nambu mechanics is constructed by using the differential forms and exterior derivatives of fractional orders. The generalized Pfaffian equations are obtained and one example is investigated in details. On leave of absence from Institute of Space Sciences, P.O. Box, MG-23, 76900, Magurele-Bucharest, Romania.     

The Hyers-Ulam stability of nonlinear recurrences

We show some Hyers-Ulam type stability results for some nonlinear recurrences in metric spaces.     

Electronic and topological investigation of growth-regulating activity in the series of abscisic acid analogs

The structure-reactivity relationship in the series of abscisic acid analogs was investigated by means of the electronic structure parameters. The fragments of the molecules responsible for the activity (inactivity) in the investigated series of chemical compounds were determined by means of the electronic topological approach. The developed forecasting system makes it possible to undertake a purposeful search for new potentially active compounds.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 5, pp. 590–594, September–October, 1989.     

Thermogravimetric characterization of styrene–divinylbenzene copolymers containing alpha-isopropylaminophosphonic acid groups

A commercial styrene–divinylbenzene copolymer was functionalized by multistep reactions with alpha-isopropylaminophosphonic acid groups. Three different functionalized copolymers were obtained in which the phosphonic groups are in meta (1E), para (2E), and ortho (3E) positions. The thermal behavior was studied using the TG/IR hyphenated technique and kinetic analysis of thermo-oxidation under nonisothermal conditions. The evolved gas analysis confirms the partial thermo-oxidative degradation of polymeric materials, with significant preservation of the aromatic ring. The kinetic analysis was performed by three methods: Friedman, Flynn–Wall–Ozawa, and nonparametric kinetic.