This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenzlike system. The analytical conditions for the synchronization of these pairs of different fractional order ch...

In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name „state“ space for the integer-order and fractional-order system and the importance of the initialization function for the fractionalorder system. Some implications concernin...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

We show experimentally that diffraction-induced surface plasmon excitation can mimic enhanced transmission and cause a highly sensitive modulation by the coherent interference between zero-order and reflected first-order diffraction in select regions of the terahertz spectrum. Based on the study of a one-dimensional metallic grating, we obtain the physical mechanisms of the fractional-order sur...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...

In this paper, we first establish decay estimates for the fractional and higher-order H\'enon-Lane-Emden systems by using a nonlocal average integral estimates, which deduce result of non-existence. Next, apply method scaling spheres introduced in \cite{DQ2} to derive Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).