<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.</p></abstract>

In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.

Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients

Laboratory of Fundamental and Numerical Mathematics

Departement of Mathematics, Faculty of Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear...

Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients

Published Online: Aug 17, 2019

Page range: 99 - 116

Received: May 31, 2018

DOI: https://doi.org/10.2478/ausm-2019-0009

Keywords
nonlinear time-fractional wave-like equations, Caputo fractional derivative, fractional natural decomposition method, Adomian polynomials

© 2019 Ali Khalouta et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients

Published Online: Aug 17, 2019

Page range: 99 - 116

Received: May 31, 2018

DOI: https://doi.org/10.2478/ausm-2019-0009

Keywordsnonlinear time-fractional wave-like equations, Caputo fractional derivative, fractional natural decomposition method, Adomian polynomials

© 2019 Ali Khalouta et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear time-fractional wave-like equations, Caputo fractional derivative, fractional natural decomposition method, Adomian polynomials