Nonlinear Dynamics

, Volume 94, Issue 3, pp 1819–1834 | Cite as

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

  • Omar Abu ArqubEmail author
  • Zaid Odibat
  • Mohammed Al-Smadi
Original Paper


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.


Hilbert space Fractional modeling Partial integrodifferential equation Robin functions types Fredholm–Volterra operator 



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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAl-Balqa Applied UniversitySaltJordan
  2. 2.School of Basic Sciences and HumanitiesGerman Jordanian UniversityAmmanJordan
  3. 3.Department of Applied Science, Ajloun CollegeAl-Balqa Applied UniversityAjlounJordan

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