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Numerical solution of a class of Caputo–Fabrizio derivative problem using Haar wavelet collocation method

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Abstract

In this paper, we propose an efficient numerical method to solve a class of fractional differential equations with Caputo–Fabrizio fractional derivative. This method is based on Haar wavelet collocation method to convert the considered problem to an algebraic system of equations. The main advantage of our proposed method is its accuracy and exponential convergence which is proved by error analysis. Finally, illustative examples are provided to demontrate the efficiency of our method.

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Acknowledgements

The authors are highly grateful to the anonymous referee for his/her valuable comments and suggestions for the improvement of the paper.

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Author notes

  1. Bachir Dehda, Abdelaziz Azeb Ahmed, Fares Yazid and Fatima Siham Djeradi have contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Operator Theory and PDE: Foundations and Applications, University of El Oued, 39000, El Oued, Algeria

    Bachir Dehda & Abdelaziz Azeb Ahmed

  2. Laboratory of Pure and Applied Mathematics, Amar Telidji University, 03000, Laghouat, Algeria

    Fares Yazid & Fatima Siham Djeradi

Authors
  1. Bachir Dehda
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  2. Abdelaziz Azeb Ahmed
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  3. Fares Yazid
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  4. Fatima Siham Djeradi
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Correspondence to Fares Yazid.

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Dehda, B., Azeb Ahmed, A., Yazid, F. et al. Numerical solution of a class of Caputo–Fabrizio derivative problem using Haar wavelet collocation method. J. Appl. Math. Comput. 69, 2761–2774 (2023). https://doi.org/10.1007/s12190-023-01859-7

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  • DOI: https://doi.org/10.1007/s12190-023-01859-7

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