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Shifted Vieta‐Fibonacci polynomials for the fractal‐fractional fifth‐order KdV equation
Author(s) -
Heydari M. H.,
Avazzadeh Z.,
Atangana A.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7219
Subject(s) - mathematics , korteweg–de vries equation , fibonacci number , fractal , algebraic equation , power series , fibonacci polynomials , classical orthogonal polynomials , order (exchange) , series (stratigraphy) , mathematical analysis , pure mathematics , orthogonal polynomials , discrete mathematics , nonlinear system , paleontology , physics , finance , quantum mechanics , economics , biology
In this article, the fractal‐fractional (FF) version of the fifth‐order KdV equation is introduced. The shifted Vieta‐Fibonacci (VF) polynomials are generated and adopted to establish a simple and accurate numerical method for solving this equation. To this end, the operational matrices of ordinary and FF derivatives of these polynomials are obtained in explicit forms. These matrices together with the series expansion of the shifted VF polynomials are mutually utilized to convert the original equation into a system of algebraic equations which is much easier. Some numerical examples are examined to show the power and accuracy of the method.