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Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems

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Abstract

This paper studies the variable fractional functional boundary value problems (VFF–BVPs) by considering Caputo fractional derivative. We use the reproducing kernel method (RKM) without the orthogonalization process as a smart scheme. For this purpose, we construct a reproducing kernel that does not satisfy the boundary condition of VFF–BVP. With this kernel, we can better approximate the solutions for VFF–BVP. Using this method increases the accuracy of the approximate solution so that a significant error analysis can be produced. Finally, two numerical examples are solved to illustrate the efficiency of the present method.

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Acknowledgements

We thank the anonymous reviewers for helpful comments, which lead to definite improvement in the manuscript.

Funding

The authors declare that this research received no grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Hajar Rasekhinezhad & Tofigh Allahviranloo

  2. Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

    Saeid Abbasbandy

  3. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey

    Tofigh Allahviranloo

  4. Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

    Esmail Baboliand

Authors
  1. Hajar Rasekhinezhad
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  2. Saeid Abbasbandy
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  3. Tofigh Allahviranloo
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  4. Esmail Baboliand
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I confirm that all authors listed on the title page have contributed significantly to the work, have read the manuscript, attest to the validity and legitimacy of the data and its interpretation, and agree to its submission.

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Correspondence to Saeid Abbasbandy.

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Rasekhinezhad, H., Abbasbandy, S., Allahviranloo, T. et al. Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems. Int. J. Dynam. Control (2024). https://doi.org/10.1007/s40435-024-01397-5

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  • DOI: https://doi.org/10.1007/s40435-024-01397-5

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