Applications of variational iteration and homotopy perturbation methods to obtain exact solutions for time-fractional diffusion-wave equations

作者：Ates Inan^*; Yildirirn Ahmet

来源：International Journal of Numerical Methods for Heat and Fluid Flow, 2010, 20(6-7): 638-654.

DOI：10.1108/09615531011056809

• Differential equations
• Iterative methods
• Flow
• Heat
• Numerical analysis

Purpose - The purpose of this paper is to consider the time-fractional diffusion-wave equation. The time-fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order alpha is an element of (0, 2]. The fractional derivatives are described in the Caputo sense.
Design/methodology/approach - The two methods in applied mathematics can be used as alternative methods for obtaining an analytic and approximate solution for different types of differential equations.
Findings - Four examples are presented to show the application of the present techniques. In these schemes, the solution takes the form of a convergent series with easily computable components. The present methods perform extremely well in terms of efficiency and simplicity.
Originality/value - In this paper, the variational iteration and homotopy perturbation methods are used to obtain a solution of a fractional diffusion equation.

• 出版日期2010