A fractional time derivative is introduced into Burger’s equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the fractional derivative is adopted here, replacing this nonlocal operator by a continuum of memory variables that satisfy local-in-time ordinary differential equation...

In the present paper we consider problems modeled by the following non-local fractional equation { (−∆)u− λu = μf(x, u) in Ω u = 0 in R \ Ω , where s ∈ (0, 1) is fixed, (−∆) is the fractional Laplace operator, λ and μ are real parameters, Ω is an open bounded subset of R, n > 2s , with Lipschitz boundary and f is a function satisfying suitable regularity and growth conditions. A critical point ...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

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...