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A pair of van der Pol oscillators coupled by fractional derivatives
Fractional calculus Fractional derivative Coupled oscillators Perturbation methods
2015/8/27
Weconsiderthestabilityofthein-phaseand out-of-phase modes of a pair of fractionally-coupled van der Pol oscillators:x ?? −? ? 1−x 2 ? x ? +x = ?γ D α (y −x) (1)y ?? −? ? 1ͨ...
Hamiltonian Formulation of Classical Fields with Fractional Derivatives
Fractional derivatives Lagrangian and Hamiltonian formulation
2011/8/3
Abstract: An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical...
Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform
fractional derivatives and integrals time scales Laplace transform
2011/1/19
We introduce a fractional calculus on time scales using the theory of delta (or nabla)dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary ...
Cosmological Models with Fractional Derivatives and Fractional Action Functional
Fractional Derivative and Integral Cosmology
2010/12/20
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact sol...
A note on the definition of fractional derivatives applied in rheology
Fractional derivatives Rheology Riemann–Liouville definition Caputo definition
2012/2/28
It is known that there exist obivious differences between the two most commonly used definitions of fractional derivatives—Riemann–Liouville (R–L) definition and Caputo definition. The multiple defini...
FRACTIONAL DERIVATIVES OF LOCAL TIMES OF STABLE LEVY PROCESSES AS THE LIMITS OF THE OCCUPATION TIME PROBLEM IN BESOV SPACE
Stable processes local time fractional derivative occupittion time problem Besov space
2009/9/21
In this paper, we firstly study the Besov regularity of
the local time of symmetric stable processes and of its fractional derivative.
Secondly, we establish Limit theorems for occupation times of
...
Integral Means Inequalities for Fractional Derivatives of Some General Subclasses of Analytic Functions
Integral means inequalities Fractional derivatives Analytic functions Univalent functions Extreme points Subordination
2008/6/30
Integral Means Inequalities for Fractional Derivatives of Some General Subclasses of Analytic Functions.
Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
Distortion inequalities analytic functions fractional derivatives univalent functions convex functions hypergeometric function
2008/6/27
Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions.
Fractional derivatives of random walks: Time series with long-time memory
Fractional derivatives random walks Time series long-time memory
2010/12/20
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochas...