<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This work presents a numerical comparison between two efficient methods namely the fractional natural variational iteration method (FNVIM) and the fractional natural homotopy perturbation method (FNHPM) to solve a certain type of nonlinear Caputo time-fractional partial differential equations in particular, nonlinear Caputo time-fractional wave-like equations with variable coefficients. These two methods provided an accurate and efficient tool for solving this type of equations. To show the efficiency and capability of the proposed methods we have solved some numerical examples. The results show that there is an excellent agreement between the series solutions obtained by these two methods. However, the FNVIM has an advantage over FNHPM because it takes less time to solve this type of nonlinear problems without using He’s polynomials. In addition, the FNVIM enables us to overcome the diffi-culties arising in identifying the general Lagrange multiplier and it may be considered as an added advantage of this technique compared to the FNHPM.</p></abstract>

This work presents a numerical comparison between two efficient methods namely the fractional natural variational iteration method (FNVIM) and the fractional natural homotopy perturbation method (FNHPM) to solve a certain type of nonlinear Caputo time-fractional partial differential equations in particular, nonlinear Caputo time-fractional wave-like equations with variable coefficients. These two methods provided an accurate and efficient tool for solving this type of equations. To show the efficiency and capability of the proposed methods we have solved some numerical examples. The results show that there is an excellent agreement between the series solutions obtained by these two methods. However, the FNVIM has an advantage over FNHPM because it takes less time to solve this type of nonlinear problems without using He’s polynomials. In addition, the FNVIM enables us to overcome the diffi-culties arising in identifying the general Lagrange multiplier and it may be considered as an added advantage of this technique compared to the FNHPM.

Numerical Comparison of FNVIM and FNHPM for Solving a Certain Type of Nonlinear Caputo Time-Fractional Partial Differential Equations

Laboratory of Fundamental Mathematics and Numerical, Department of Mathematics, Faculty of Sciences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

This work presents a numerical comparison between two efficient methods namely the fractional natural variational iteration method (FNVIM) and the fractional...

Numerical Comparison of FNVIM and FNHPM for Solving a Certain Type of Nonlinear Caputo Time-Fractional Partial Differential Equations

Published Online: Jul 09, 2020

Page range: 203 - 221

Received: Aug 19, 2019

Accepted: Jun 03, 2020

DOI: https://doi.org/10.2478/amsil-2020-0008

Keywords
nonlinear Caputo time-fractional partial differential equations, Caputo fractional derivative, natural transform, variational iteration method, homotopy perturbation method

© 2020 Ali Khalouta et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Numerical Comparison of FNVIM and FNHPM for Solving a Certain Type of Nonlinear Caputo Time-Fractional Partial Differential Equations

Published Online: Jul 09, 2020

Page range: 203 - 221

Received: Aug 19, 2019

Accepted: Jun 03, 2020

DOI: https://doi.org/10.2478/amsil-2020-0008

Keywordsnonlinear Caputo time-fractional partial differential equations, Caputo fractional derivative, natural transform, variational iteration method, homotopy perturbation method

© 2020 Ali Khalouta et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
nonlinear Caputo time-fractional partial differential equations, Caputo fractional derivative, natural transform, variational iteration method, homotopy perturbation method