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Numerical solution of Bagley–Torvik equations using Legendre artificial neural network method

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Abstract

In this article, we have used the Legendre artificial neural network to find the solution of the Bagley–Torvik equation, which is a fractional-order ordinary differential equation. Caputo fractional derivative has been considered throughout the presented work to handle the fractional order differential equation. The training of optimal weights of the network has been carried out using a simulated annealing optimization technique. Here we have presented three examples to exhibit the precision and relevance of the proposed technique with comparison to the other numerical methods with error analysis. The proposed technique is an easy, highly efficient, and robust technique for finding the approximate solution of fractional-order ordinary differential equations.

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Acknowledgements

The authors are grateful to the National Board of Higher Mathematics (NBHM), Government of India for providing financial support to carry out this work through its Project sanctioned Order No. 02011/25/2019/R&D/7351. We express our sincere thanks to editor in chief, editor and reviewers for their valuable suggestions to revised this manuscript.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, U.P., 211004, India

    Akanksha Verma & Manoj Kumar

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  1. Akanksha Verma
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  2. Manoj Kumar
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Correspondence to Akanksha Verma.

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Verma, A., Kumar, M. Numerical solution of Bagley–Torvik equations using Legendre artificial neural network method. Evol. Intel. 14, 2027–2037 (2021). https://doi.org/10.1007/s12065-020-00481-x

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  • DOI: https://doi.org/10.1007/s12065-020-00481-x

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