Fourier spectral method for solving fractional-in-space variable coefficient KdV-Burgers equation

Numerical Simulation of Soliton Propagation Behavior for the Fractional-in-Space NLSE with Variable Coefficients on Unbounded Domain

“…In [28], authors developed a regularized Lie-Trotter splitting FSM to study the fractional-in-space regularized logarithmic NLSE. Wang et al [29,30] have used the FSM to investigate a class of fraction-in-space standard KdV-modified KdV equations and fractional reaction-diffusion models. It should be noted that the FSM generally defaults its boundary condition to a periodic boundary; that is, the function value at one end of the boundary will affect the function value at the other end of the boundary.…”

An efficient numerical simulation of chaos dynamical behaviors for fractional-order Rössler chaotic systems with Caputo fractional derivative

“…Some fractional derivative [9][10][11] and corresponding numerical method have been widely employed in numerical solution of fractal-fractional systems, [12][13][14][15] such as Adams-Bashforth-Moulton algorithm, 1 predictor-correctors scheme, 2 highprecision difference scheme, 16,17 local discontinuous Galerkin method, 18 finite difference method, 19,20 reproducing kernel method, 21,22,23 spectral method, [24][25][26][27] homotopy perturbation method, [28][29][30] Li-He's modified homotopy perturbation method, 31,32 and variational iteration method. The variational iteration method was proposed by Ji-huan He and was applied to a kind of nonlinear oscillators, 33,34 autonomous ordinary differential systems, 35 the Kaup-Newell system, 36 the nanobeam-based N/MEMS system, 37 and fractal pull-in motion of electrostatic MEMS resonators.…”