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Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates

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Abstract

This paper introduces an efficient numerical algorithm for solving a significant class of linear and nonlinear time-fractional partial differential equation governed by Fredholm–Volterra operator in the sense of Robin conditions. A direct approach based on the normalized orthonormal function systems that fitted from the Gram–Schmidt orthogonalization process is utilized to transcribe the problem under study into appropriate Hilbert space. Some functional analysis theories such as upper error bound and convergence behavior under some assumptions which give the hypothetical premise of the proposed calculation are likewise talked about. Mathematical properties of the numerical results obtained are analyzed as well as general features of many numerical solutions have been identified. At long last, the used outcomes demonstrate that the present calculation and mimicked toughening give a decent planning procedure to such models.

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Acknowledgements

The authors would like to express their gratitude to the unknown referees for carefully reading the paper and their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, 19117, Jordan

    Omar Abu Arqub

  2. School of Basic Sciences and Humanities, German Jordanian University, Amman, 11180, Jordan

    Zaid Odibat

  3. Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, 26816, Jordan

    Mohammed Al-Smadi

Authors
  1. Omar Abu Arqub
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  2. Zaid Odibat
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  3. Mohammed Al-Smadi
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Correspondence to Omar Abu Arqub.

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Abu Arqub, O., Odibat, Z. & Al-Smadi, M. Numerical solutions of time-fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates. Nonlinear Dyn 94, 1819–1834 (2018). https://doi.org/10.1007/s11071-018-4459-8

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  • DOI: https://doi.org/10.1007/s11071-018-4459-8

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