Search results for "Fractional order"
showing 5 items of 5 documents
Existence of a traveling wave solution in a free interface problem with fractional order kinetics
2021
Abstract In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 α 1 . We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincare-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is fin…
A state-space approach to dynamic stability of fractional-order systems: The extended Routh-Hurwitz theorem
2017
This paper considers the case of Beck’s column, a linear elastic cantilever column subjected to a constant follower load at its free end. The column foundation is modeled as bed of hereditary elements that react with a vertical force distributed along the beam axis. The reacting supports are modeled with spring-pot element that is a two parameters mechanical elements (C; ) with an intermediate behavior between spring and dashpot. The constitutive equation of the spring-pot involves the so called fractional order derivatives and dynamic stability problem in presence of fractional-order operator must be faced for the Beck’s column. In this study , the authors generalize Routh-Hurwitz theorem …
Simulation d'un modèle à dérivée fractionnaire décrivant l'activité électrique des cellules béta du pancréas
2018
National audience; Dans cette communication, nous rappelons tout d’abord les différents régimes de fonctionnement dumodèle de Pernarowski. Ce dernier permet de décrire l’activité électrique des céllules béta du pancréas. Par la suite,nous définissons le modèle à dérivées fractionnaires. En particulier, le schéma d’intégration numérique choisipour résoudre le système d’équations à dérivée fractionnaire est intégralement présenté. Notre analyse montrequ’avec ce modèle fractionnaire, l’activité électrique peut être contrôlée par l’ordre des dérivées fractionnaires ;ce qui pourraît rendre compte de certains dysfonctionnement dans la sécrétion de l’insuline par les céllules béta dupancréas.
Free energy and states of fractional-order hereditariness
2014
AbstractComplex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
2018
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.