A hybrid analytical algorithm for nonlinear fractional wave-like equations

• Published in: Mathematical modelling of natural phenomena Vol. 14; no. 3; p. 304
• Main Authors: Kumar, Devendra, Singh, Jagdev, Purohit, Sunil Dutt, Swroop, Ram
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2019
• Subjects: 26A33; 35L05; 35R11; Algorithms; Computational fluid dynamics; Computer applications; Economic models; HATM; Mathematical models; Nonlinear analysis; Nonlinear equations; Nonlinear wave-like equation of fractional order; numerical solution; Perturbation; Stochastic systems; Variation
• ISSN: 0973-5348; 1760-6101
• DOI: 10.1051/mmnp/2018063

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.