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An innovative Vieta–Fibonacci wavelet collocation method for the numerical solution of three-component Brusselator reaction diffusion system of fractional order

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Abstract

The research article presents a novel approach for the numerical solution of three-component time fractional order Brusselator reaction-diffusion system using the innovative Vieta–Fibonacci wavelet and collocation method. The proposed method involves the derivation of operational matrices for both integer and fractional order derivatives, enable the accurate and efficient computation of the system. The existence, uniqueness of solution and Ulam–Hyers stability of the model are rigorously discussed. Furthermore, a comprehensive convergence analysis of the Vieta–Fibonacci wavelet method is presented, which demonstrates its effectiveness in approximating the fractional derivative of the Brusselator system. The numerical experiments showcase the superior performance of the method in terms of accuracy and computational efficiency. The application of the Vieta–Fibonacci wavelet method to the three-component fractional order Brusselator reaction-diffusion system marks a significant advancement in the field of computational mathematics. The successful implementation of the Vieta–Fibonacci wavelet method signifies a significant advancement in solving fractional-order reaction-diffusion problems.

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Acknowledgements

The authors are extending their heartfelt thanks to the reviewers for their positive suggestions to improve the quality of the revised article.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005, India

    Manpal Singh, S. Das &  Rajeev

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  1. Manpal Singh
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  3. Rajeev
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Correspondence to Manpal Singh.

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Singh, M., Das, S. & Rajeev An innovative Vieta–Fibonacci wavelet collocation method for the numerical solution of three-component Brusselator reaction diffusion system of fractional order. J Math Chem 62, 1558–1594 (2024). https://doi.org/10.1007/s10910-024-01621-9

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