Liao’s method for a few space and time fractional reaction-diffusion equations arising in Engineering
نویسندگان
چکیده
Abstract— In this paper, we have applied an accurate and efficient homotopy analysis method (HAM) to find the approximate/analytical solutions for space and time fractional reactiondiffusion equations arising in mathematical chemistry. The method provides solutions in rapid convergence series with computable terms. To the best of our knowledge, until now there is no rigorous HAM solutions have been reported for the space and time fractional reaction-diffusion equations (FRDEs). Some numerical examples are presented to demonstrate the validity and applicability of the method. The power of the manageable method is confirmed. Moreover, the use of HAM is found to be accurate, efficient, simple, flexible and less computation cost. KeywordHomotopy analysis method, fractional derivatives, space and time fractional reaction diffusion equations
منابع مشابه
An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...
متن کاملSolving large systems arising from fractional models by preconditioned methods
This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...
متن کاملA new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...
متن کاملSolving nonlinear space-time fractional differential equations via ansatz method
In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...
متن کاملNumerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method
In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...
متن کامل