Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part IIOpen Access

APPROXIMATE SOLUTION OF FORNBERG–WHITHAM EQUATION BY MODIFIED HOMOTOPY PERTURBATION METHOD UNDER NON-SINGULAR FRACTIONAL DERIVATIVE

HUSSAM ALRABAIAH

HUSSAM ALRABAIAH

College of Engineering, Al Ain University, Al Ain, UAE

Mathematics Department, Tafila Technical University, Tafila, Jordan

E-mail Address: hussam.alrabaiah@aau.ac.ae

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https://doi.org/10.1142/S0218348X22400291Cited by:2 (Source: Crossref)

Abstract

The basic idea of this paper is to investigate the approximate solution to a well-known Fornberg–Whitham equation of arbitrary order. We consider the stated problem under $ABC$ fractional order derivative. The proposed derivative is non-local and contains non-singular kernel of Mittag-Leffler type. With the help of Modified Homotopy Perturbation Method (MHPM), we find approximate solution to the aforesaid equations. The required solution is computed in the form of infinite series. The method needs no discretization or collocation and easy to implement to compute the approximate solution that we intend. We also compare our results with that of the exact solution for the initial four terms approximate solution as well as with that computed by the Laplace decomposition method. We also plot the approximate solution of considered model through surface plots. For numerical illustration, we use Matlab throughout this work.

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Vol. 30, No. 01

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History

Received 4 February 2021

Accepted 22 August 2021

Published: October 27, 2021

Information

This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part II”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Khan Muhammad (Sejong University, South Korea), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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APPROXIMATE SOLUTION OF FORNBERG–WHITHAM EQUATION BY MODIFIED HOMOTOPY PERTURBATION METHOD UNDER NON-SINGULAR FRACTIONAL DERIVATIVE

Abstract

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