[PDF] Top 20 A fast numerical method for fractional partial differential equations

... for fractional differential ...variable-order fractional operators with applications can be found in ...for fractional terminal value problems with non-smooth solutions can be found in ... See full document

... collocation method is considered to develop an approximate scheme to solve fractional delay differential equations ...of fractional order derivatives, the challenge of these methods is ... See full document

... decomposition method. This method was introduced in the 1980s by George Adomian (1923-1996), and it was applied to many problems ( [1]- ...decomposition method was coupled with Laplace transform ... See full document

... The structure of the current paper is as follows. For easy reader-friendly reference, some basic definitions and properties of fractional differential equations are presented in Section 2. In Section ... See full document

... In the present work, we introduce a blend of Natural transform and homotopy perturbation method. We explored the methodology for the construction of the new twisting scheme and employed to compute the analytic ... See full document

... ADM is very acceptable method to solve FFDE. The aim of this paper is to technique of findings the numerical solution of some liner fractional differential equation with initial fuzzy value ... See full document

... the numerical point of view, such as the Legendre wavelet method, the spectral method and quartered shifted Legendre method based on Gauss ...Euler’s method has been proven to be ... See full document

... new numerical method for solving the fractional Riccati differential equation is ...The fractional derivatives are described in the Caputo sense. The method is based upon ... See full document

... quadrature method to the solution of a fractional-order Riccati differential ...The fractional derivative is described in the Caputo ...of fractional derivatives to reduce a Riccati differential ... See full document

... FD method belongs to the general class of grid-based differential numerical modelling methods (finite difference ...Maxwell's equations are discretised using central-difference approximations ... See full document

... new fractional Jacobi elliptic equation method to seek exact solutions of fractional partial differential ...certain fractional partial differential equation can be turned into ... See full document

... 2.1. Fractional calculus. There are several definitions of a fractional derivative of order α > 0 (see [9], [10], ...the fractional calculus theory which are used further in this ... See full document

... and fractional derivative is in Riemann-Liouville ...Euler method for the fractional differential ...specific numerical examples equipped with comparing figure of numerical ... See full document

... second fractional complex transformations for ...nonlinear fractional complex transformations, it is worth to investigate the applications of other algebraic methods to fractional partial ... See full document

... differential equations are considered. From the numerical result, we can find that the Adomian decomposition method is an efficient ...the numerical result has high precision. In ... See full document

... above problem is u(x,t ) = x 2 + 2 Γ(2α Γ(α +1) +1) t 2α . Figure 4 shows the exact solution for α = 0.5. From figure 1 - 4, we can see that with J increasing, the numerical solution more and more close to the ... See full document

... differential equations are found to be an effective tool to describe certain phys- ical phenomena such as damping laws, rheology, diffusion processes, and so ...solve fractional differential ...the ... See full document

... meshless numerical scheme for solving fractional differential equations is ...collocation method. This technique plays an important role to reduce a fractional ... See full document

... of fractional order integration and differentiation, is known to provide an excellent setting for capturing in a model framework concerned with real–world problems in a variety of disciplines from physics, ... See full document

... provide fast and universal mathematical tool for obtaining the solution of PDEs or even ...present method can be readily applied to more complicated fractional differential ... See full document