Applications of variational iteration and homotopy perturbation methods to obtain exact solutions for time‐fractional diffusion‐wave equations
Makaleler > Tam Makale · 2010
Yazarlar: I˙nan Ates¸, Ahmet YILDIRIM
International Journal of Numerical Methods for Heat & Fluid Flow, Uluslararası, Wos, 2010, cilt 20, ss 638-654
DOI: 10.1108/09615531011056809
Özet
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 α ∈ (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.