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

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 ? ? (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. © Emerald Group Publishing Limited.