**Approximate Solutions of Time Fractional Diffusion Wave Models**

#### **Abdul Ghafoor 1, Sirajul Haq 2, Manzoor Hussain 2, Poom Kumam 3,4,5,\* and Muhammad Asif Jan 1**


Received: 11 July 2019; Accepted: 27 August 2019; Published: 3 October 2019

**Abstract:** In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing *L*2 and *L*∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before.

**Keywords:** fractional differential equations; two-dimensional wavelets; finite differences
