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Existence and numerical analysis using Haar wavelet for fourth-order multi-term fractional differential equations

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Abstract

In this paper, a numerical technique is developed for the solution of multi-term fractional differential equations (FDEs) upto fourth order by using Haar collocation method (HCM). In Caputo sense, the fractional derivative is defined. The integral involved in the equations is calculated by the method of Lepik. The HCM converts the given multi-term FDEs into a system of linear equations. The convergence of the proposed method HCM is checked on some problems. Mean square root and maximum absolute errors are calculated for different numbers of collocation points(CPs), which are recorded in tables. The exact and approximate solution comparison is also given in figures. The time taken by CPU for numerical results is also given in the tables.

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Acknowledgements

The authors, Kamal Shah, Nabil Mlaiki and Thabet Abdeljawad, would like to thank Prince Sultan University for support through TAS research lab.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, 25120, Pakistan

    Rohul Amin

  2. Department of Mathematics and Sciences, Prince Sultan University, P.O.Box 11586, Riyadh, Saudi Arabia

    Kamal Shah, Nabil Mlaiki & Thabet Abdeljawad

  3. Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan

    Kamal Shah

  4. Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey

    Şuayip Yüzbaşı

  5. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Thabet Abdeljawad

  6. Department of Mathematics, Karakoram International University, Hunza Campus, Gilgit-Baltistan, Pakistan

    Arshad Hussain

Authors
  1. Rohul Amin
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  2. Kamal Shah
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  3. Nabil Mlaiki
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  4. Şuayip Yüzbaşı
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  5. Thabet Abdeljawad
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  6. Arshad Hussain
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Correspondence to Rohul Amin.

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Communicated by Agnieszka Malinowska.

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Amin, R., Shah, K., Mlaiki, N. et al. Existence and numerical analysis using Haar wavelet for fourth-order multi-term fractional differential equations. Comp. Appl. Math. 41, 329 (2022). https://doi.org/10.1007/s40314-022-02041-8

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  • DOI: https://doi.org/10.1007/s40314-022-02041-8

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