[PDF] Top 20 Fourier Spectral Method for Solving Fractional order System

... The reaction-diffusion model (2) has been shown in [38] to have a unique and globally stable attractor. A lot of two- species models with various functional responses or Holling type-II, reaction-diffusions, and delays ... See full document

... time fractional derivative of variable ...first order temporal accuracy and first order spatial accuracy is developed in ...for solving partial differential equations with fractional ... See full document

... with fractional systems ,so the propose technique provide a good results for linear system of fractional integro- differential ...solve fractional linear integro-differential equations ,which ... See full document

... efficient spectral tau and collocation method based on the Chebyshev poly- nomials for solving this ...tau method based on the shifted Legendre Gauss-Lobbato quadrature is used for ... See full document

... element method is presented in [6, ...mortar spectral elements method for the Strang and Fix algorithm [9] in the case of the biharmonic ...matrix system, then we use the conjugate gradient ... See full document

... current spectral method, such as the Galerkin, tau, and pseudospectral methods can be found in the ‘weighted residual method’ of Finlayson and Scriven ...Nowadays, spectral methods are efficient ... See full document

... of fractional diffusion models have been increasingly noticeable in ...time fractional diffusion equation in whole space and also in half ...time fractional diffusion equation by implicit finite ... See full document

... Recently, fractional initial and boundary value problems have been studied ...and Fourier transforms [1, 2], Adomian decomposition and variational iteration methods [3, 4], eigenvector expansion [5], ... See full document

... integer order integration and differentiation to its non-integer (fractional) order counterpart, has proved to be a valuable tool in the modeling of many phenomena in the fields of physics, ... See full document

... Chebyshev spectral collocation method (often called pseudo-spectral) is used in this ...spatial fractional de- rivatives are easily computed and a system of ordinary differential ... See full document

... Transformation Method (GDTM) is used to solve volterra’s model for population growth of a species within a closed ...prescribed method for this real life application shows it so fast and ...transformation ... See full document

... approximate fractional differential equations, such as Adomian decomposition method [17], variational iteration method [18], homotopy analysis method [19] and collocation method ... See full document

... new method by using FrFT and multifractal theory to do low- resolution radar target ...in order to determine the optimal transform Fourier domains of FrFT and then adopt the multifractal theory to ... See full document

... and spectral methods for partial differential equations [1, 2, 3, ...of fractional order [5, 6, 7, ...integer order to fractional type of these problems [10, ...of fractional ... See full document

... the fractional calculus theory, in section 3 the Jacobi polynomial, and its properties are ...explicit system of linear algebraic ...proposed method, concluding remarks are given in the last ... See full document

... m = with the final time T = 2 are given. Also, in Figure 1 and Figure 2, comparison between the exact solution and the approximate solution at T = 0.5 with time step τ = 0.0025 , m = 3 and m = 5 , are presented, ... See full document

... 3.2. Adaptive exponential time differencing. Exponential time differencing (ETD) schemes have a long history in the field of computational electrodynamics [32]. They have since gained tremendous attentions in various ... See full document

... Fortunately, fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous ...Subsequently, fractional diffusion equations have been applied in ... See full document

... of fractional order derivatives and the terms contain linear functional argument which are taken to be multi-term of fractional order derivatives as ...of fractional derivatives are ... See full document

... teger order has been a hot topic in numerical and compu- tational mathematics for a long ...of fractional differential equations has been recently studied by numerous ...general fractional ... See full document