A hybrid analytical algorithm for nonlinear fractional wave-like equations

¹ Department of Mathematics, University of Rajasthan, Jaipur 302004, India.
² Department of Mathematics, JECRC University, Jaipur 303905, India.
³ Department of HEAS (Mathematics), Rajasthan Technical University, Kota 324010, India.
⁴ Department of Mathematics, Arya Institute of Engineering & Technology, Jaipur 303101, India.

^* Corresponding author: sunil_a_purohit@yahoo.com

Received: 14 September 2018
Accepted: 9 October 2018

Abstract

In this work, we aim to present a hybrid numerical scheme based on the homotopy analysis transform method (HATM) to examine the fractional model of nonlinear wave-like equations having variable coefficients, which narrate the evolution of stochastic systems. The wave-like equation models the erratic motions of small particles that are dipped in fluids and fluctuations of the stochastic behavior of exchange rates. The uniqueness and existence of HATM solution have also been discussed. Some numerical examples are given to establish the accurateness and effectiveness of the suggested scheme. Furthermore, we show that the proposed computational approach can give much better approximation than perturbation and Adomain decomposition method, which are the special cases of HATM. The result exhibits that the HATM is very productive, straight out and computationally very attractive.