Mandelbrot set and Julia sets of fractional order
In this paper the fractional-order Mandelbrot and Julia sets in the sense of q -th Caputo-like discrete fractional diﬀerences, for q ∈ (0 , 1), are introduced and several properties are analytically…
SHOWING 1-10 OF 43 REFERENCES
Comments on “Discrete fractional logistic map and its chaos” [Nonlinear Dyn. 75, 283–287 (2014)]
- MathematicsNonlinear Dynamics
In this note, two comments are pointed out to the paper (Wu and Baleanu in Nonlinear Dyn 75:283–287, 2014). It is confirmed that the equation of fractional logistic map proposed by Wu and Baleanu…
Initial value problems in discrete fractional calculus
This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first…
On fractional–order discrete–time systems: Chaos, stabilization and synchronization
- MathematicsChaos, Solitons & Fractals
Fractional-order PWC systems without zero Lyapunov exponents
In this paper, it is shown numerically that a class of fractional-order piece-wise continuous systems, which depend on a single real bifurcation parameter, have no zero Lyapunov exponents but can be…
The discrete fractional duffing system: Chaos, 0-1 test, C0 complexity, entropy, and control.
Through phase plots, bifurcation diagrams, and Lyapunov exponents, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors.
A proof for non existence of periodic solutions in time invariant fractional order systems
Discrete chaos in fractional delayed logistic maps
Recently the discrete fractional calculus (DFC) started to gain much importance due to its applications to the mathematical modeling of real world phenomena with memory effect. In this paper, the…
Caputo standard α-family of maps: fractional difference vs. fractional.
Property of fractional difference maps (systems with falling factorial-law memory) are similar to the properties of fractionAL maps ( systems with power- Law memory) and differences in properties of falling Factorial- and power- law memory maps are investigated.
Chaos, control, and synchronization in some fractional-order difference equations
- MathematicsAdvances in Difference Equations
In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by…