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Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method

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Abstract

Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is used to write the emerging operational matrices. These matrices are developed and evaluated by using the properties of VLPs. The residuated functions are mapped to zero by the tools of the Tau algorithm. Convergence and error analysis are thoroughly explored. Test examples for a fractional system of differential equations are borrowed from literature. The theoretical and simulated exercise on these examples authenticate the relevance of this scheme. Here, novel inclusion of Vieta-Lucas polynomials has been ensured in combination with the Tau approach. The operational matrix approach which provides extensive information about the fractional derivatives of different terms of Vieta-Lucas polynomial expansion, is ensured to operate to reduce the problem into an algebraic setup. The novelty is further enhanced by comparing the present scheme with the fourth-order Runge–Kutta method.

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Acknowledgements

The authors are deeply grateful to the reviewers for carefully reading the paper towards the significant improvement in the quality and presentation of the manuscript.

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Authors and Affiliations

  1. Srinivasa Ramanujan Department of Mathematics, Central University of Himachal Pradesh, Shahpur Campus, Shahpur, 176206, H.P., India

    Rahul Chaudhary, Shivani Aeri, Anu Bala & Rakesh Kumar

  2. Department of Mathematics, Cankaya University, Ankara, 06810, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Rahul Chaudhary
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  2. Shivani Aeri
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  3. Anu Bala
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  4. Rakesh Kumar
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  5. Dumitru Baleanu
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1,2,3 write the manuscript. 4 supervise the work. All authors reviewed the manuscript.

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Correspondence to Shivani Aeri.

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Chaudhary, R., Aeri, S., Bala, A. et al. Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method. Int. J. Appl. Comput. Math 10, 14 (2024). https://doi.org/10.1007/s40819-023-01656-7

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