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A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves. (English) Zbl 1388.35212
Summary: The key purpose of the present work is to constitute a numerical scheme based on \(q\)-homotopy analysis transform method to examine the fractional model of regularized long-wave equation. The regularized long-wave equation explains the shallow water waves and ion acoustic waves in plasma. The proposed technique is a mixture of \(q\)-homotopy analysis method, Laplace transform, and homotopy polynomials. The convergence analysis of the suggested scheme is verified. The scheme provides \(\hslash\) and \(n\)-curves, which show that the range convergence of series solution is not a local point effects and elucidate that it is superior to homotopy analysis method and other analytical approaches.

MSC:
35R11 Fractional partial differential equations
35A20 Analyticity in context of PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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