Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation

The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a non...

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Bibliographic Details
Published inDemonstratio mathematica Vol. 56; no. 1; pp. 111 - 121
Main Author El-Sayed, Adel Abd Elaziz
Format Journal Article
LanguageEnglish
Published De Gruyter 21.06.2023
Subjects
11B39
26A33
34A08
34C15
41A25
65L05
97N40
Caputo fractional operator
Duffing equation
Fractional-order operational matrix
Pell-Lucas polynomials
Tau method
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Summary:The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed method.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2022-0220