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A comparative study of three numerical schemes for solving Atangana–Baleanu fractional integro-differential equation defined in Caputo sense

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Abstract

This study contains numerical schemes namely Linear scheme, Quadratic scheme, and Quadratic–linear scheme to solve a fractional integro-differential equation using the Atangana–Baleanu derivative defined in Caputo sense. The error bounds of the schemes are obtained. We discuss four test examples to perform the numerical simulations, and the obtained numerical results ensure that the presented schemes work well and the obtained approximate solution agrees with the analytical solution. The convergence order and maximum absolute errors of the schemes are calculated and their comparative performances are discussed.

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Acknowledgements

The authors sincerely thank the reviewers for providing constructive comments for improvement of the manuscript. The first author acknowledges the financial support from the University Grants Commission, New Delhi, India under the JRF scheme.

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Authors and Affiliations

  1. Department of Mathematical sciences, Indian Institute of Technology (BHU),Varanasi, Varanasi, 221005, Uttar Pradesh, India

    Deeksha Singh, Farheen Sultana & Rajesh K. Pandey

  2. Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

    Abdon Atangana

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Abdon Atangana

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  1. Deeksha Singh
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  2. Farheen Sultana
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  3. Rajesh K. Pandey
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  4. Abdon Atangana
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Correspondence to Rajesh K. Pandey.

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Singh, D., Sultana, F., Pandey, R.K. et al. A comparative study of three numerical schemes for solving Atangana–Baleanu fractional integro-differential equation defined in Caputo sense. Engineering with Computers 38 (Suppl 1), 149–168 (2022). https://doi.org/10.1007/s00366-020-01132-6

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  • DOI: https://doi.org/10.1007/s00366-020-01132-6

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