相关论文: Fractional Stability
In this work we argue about the Lesche stability of some systems, that are motivated by the use of fractional derivatives.
We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.
This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts,…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe…
The existence and stability results for a class of fractional differential equations involving generalized Katugampola derivative are presented herein. Some fixed point theorems are used and enlightening examples of obtained result are also…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common…
We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the…
It is well known that the Leibniz rule for the integer derivative of order one does not hold for the fractional derivative case when the fractional order lies between 0 and 1. Thus it poses a great difficulty in the calculation of…
This paper presents some new propositions related to the fractional order $h$-difference operators, for the case of general quadratic forms and for the polynomial type, which allow proving the stability of fractional order $h$-difference…
H\"older functions represent mathematical models of nonlinear physical phenomena. This work investigates the general conditions of existence of fractional velocity as a localized generalization of ordinary derivative with regard to the…
Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are…
The stability of the zero solution of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of…