We have experimentally evidenced an elementary charge fission, in which an elementary charge in an integer quantum Hall (IQH) system breaks up into fractional charges at a local fractional quantum Hall (FQH) state. Shot-noise measurements establish the e/3-charge of tunneling quasiparticles through the local FQH state, which is prepared in a low-density region near a quantum point contact (QPC)...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel compression scheme for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our study on 1-step methods and approximate the local part of the fractional integral by integral deferred correction to enable high order accuracy...

Particle Swarm Optimization (PSO) is one of the most powerful algorithms for optimization. Traditional PSO algorithm tends to suffer from slow convergence and trapping into local optimum. In this paper, an improved PSO algorithm is proposed by combining dynamic fractional order technology and the wavelet mutation strategy. In the proposed method, a dynamic fractional order velocity update equat...