[PDF] Top 20 New Modified Method of the Chebyshev Collocation Method for Solving Fractional Diffusion Equation

... The fractional partial differential equations (FPDEs) arise in numerous problems of engineering, physics, mathematics, chemistry, biology,and viscoelasticity ( [1], [2], [3], ...[4]).Most fractional ... See full document

... decades, fractional differential equations have been paid an increasing attention as they are widely used to describe various complex phenomena in many fields such as the fluid flow, signal processing, control theory, ... See full document

... As Chebyshev polynomials and Legendre polynomials are well known family of orthogonal polynomials on the interval [−1,1] that have many applications and widely used because of their good properties in the ... See full document

... in fractional derivative problem is still new in science and engineering ...have fractional order of derivative such as in biopotential recording and functional electrical ... See full document

... a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value ...governing equation at the whole set of grid points including the boundary points ... See full document

... Integration Method (FIM) is an integral based technique, and was first introduced by Weiland in 1977 ...for solving partial differntial equations (PDEs), see for example [15, 17, 25, ...integral ... See full document

... applied collocation technique with Gauss-Lobatto nodes whereas Xie et ...tau method to determine expansion ...1D fractional diffusion equation Bahsi and Yalcinbas [10] cho- sen ... See full document

... The fractional Bagley-Torvik equation was originally formulated in a description of a real material by the use of fractional ...Bagley-Torvik equation has appeared in simulating the motion of ... See full document

... The Method of Lines Combined with Chebyshev Spectral Method respect to weighted residual (Collocation Points) for Space-Time fractional diffusion equation is considered, ... See full document

... sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is ... See full document

... on Chebyshev Tau ...Galerkin method for solving the hyperbolic telegraph ...telegraph equation. To solve the telegraph equation using the MLWS method, the conventional moving ... See full document

... the fractional sub-diffusion equation with the Neumann boundary ...spectral method was constructed by using the common L formula in time and a Legendre spectral ap- proximation in ...this ... See full document

... for solving fractional differential equations have been given such as variational iteration method [7], homotopy perturbation method [23], adomian decomposition method [8], homotopy ... See full document

... relatively new techniques used for finding solutions of fractional differential equations ...meshless method used by Liu et al. in [31] for solving time fractional ... See full document

... spectral collocation method (often called pseudo-spectral) is used in this ...the Chebyshev polynomials and Gauss-Lobbato nodes, the unknown is approximated by using the orthogonal pro- jection and ... See full document

... iterative method and in Sec. 3.2 we give a description of shifted fractional-order Legendre ...use collocation method to obtain the approx- imate solution for differential equation with ... See full document

... main equation may not be given, we have encountered an inverse ...for solving them we need to some additional measured data, see ...a fractional inverse problem which is one of the interesting and ... See full document

... iteration method [5], homotopy perturbation method [3] [6], Adomian decomposition method [7] [8], homotopy analysis method [9], collocation method [10] [11] and finite difference ... See full document

... both Equation (17). Conditions (18) and (19) are consequences of Equation (17). Therefore, every solution to (25) is in one- to-one correspondence with the solution to Equation (17). This ... See full document

... the modified HPM suggested by Momani and al. [23] for solving the time-fractional Fisher’s equation and we use the classical HPM to derive numerical solutions of the space-fractional ... See full document