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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.

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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