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A Numerical Method for Fractional Pantograph Delay Integro-Differential Equations on Haar Wavelet

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Abstract

The main objective of this research work is devoted to study the solution of fractional pantograph delay integro-differential equations based on Haar wavelet collocation (HWC) technique. Through HWC algorithm, first we reduce the underlying equations to a system of algebraic equations. After getting a system of equations, Gauss elimination method is used for the solution of the mentioned problem. Under the techniques of functional analysis, we derive the necessary conditions for the existence and uniqueness of at most one solution of the considered problem. With the help of examples taken from the literature, we investigate the validation and convergence of the HWC method. In these examples, we compare the exact and approximate solutions for different fractional orders. Through tables, errors are calculated for different nodal points, we also compare the exact and approximate solutions for different fractional orders.

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Acknowledgements

All authors are thankful to the reviewers for their careful reading of the paper and suggestions which has improved the paper very well.

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Authors and Affiliations

  1. Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan

    Israr Ahmad & Kamal Shah

  2. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

    Rohul Amin

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia

    Thabet Abdeljawad

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

    Thabet Abdeljawad

  5. Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

    Thabet Abdeljawad

Authors
  1. Israr Ahmad
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  2. Rohul Amin
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  3. Thabet Abdeljawad
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  4. Kamal Shah
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Correspondence to Thabet Abdeljawad.

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Ahmad, I., Amin, R., Abdeljawad, T. et al. A Numerical Method for Fractional Pantograph Delay Integro-Differential Equations on Haar Wavelet. Int. J. Appl. Comput. Math 7, 28 (2021). https://doi.org/10.1007/s40819-021-00963-1

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  • DOI: https://doi.org/10.1007/s40819-021-00963-1

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