On computation of solution for (2+1) dimensional fractional order general wave equation

Abstract

In this research article, we handle a class of (2+1) dimensional wave equations under fractional-order derivatives using an iterative integral transform due to Laplace. The concerned derivative is taken in the Caputo’s sense. The proposed method is a purely algebraic manipulation approach to compute solutions without a priori knowledge of geometry and physical meaning related to the proposed problem. In fact, in this procedure, we combine two novel techniques, Laplace transforms (LT) and iterative procedures to form a hybrid technique for computation of the solution to the proposed problem. The method is rapidly convergent. Here, we give various examples for the validation of our proposed method. The superiority of the method over the existing numerical method is that it does not require any prior discretization or collocation of functions. Also, the method is independent of axillary parameters as needed in the homotopy methods, because such auxiliary parameters control the efficiency of the mentioned methods. The proposed procedure is simple and straightforward. In addition, some comparison between exact and approximate solutions is also given. The proposed method is compared with the homotopy perturbation method (HPM) which shows that the proposed technique is more efficient and easy to implement.

Keywords

• Derivatives with fractional order
• Solution in series form
• Laplace transform