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

Hussam Alrabaiah
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Hussam Alrabaiah: College of Engineering, Al Ain University, Al Ain, UAE2Mathematics Department, Tafila Technical University, Tafila, Jordan

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-6

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.

Keywords: Fractional Derivative; Fornberg–Whitham Equation; Non-Singular Kernel (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400291

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