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Peer-reviewedCC BY 4.0Mathematics

Pell–Lucas Collocation Method for Time-Fractional Partial Integro-Differential Equations

  • Javad Damirchi1
  • Ahmadreza Yazdanian2
  • Shohreh Mehranpour1
  • Mahdi Mahmoudi3
  1. 1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan 35196-45399, Iran
  2. 2Faculty of Finance Sciences, Kharazmi University, Tehran 15719-14911, Iran
  3. 3Faculty of Medicine, Sigmund Freud University, 1020 Vienna, Austria
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Abstract

This paper presents a Pell–Lucas collocation method for time-fractional partial integro-differential equations (TFPIDEs) with initial and boundary conditions, where the fractional derivative is taken in the Caputo sense. The unknown solution is approximated by a truncated bivariate Pell–Lucas series, and the governing equation together with the initial and boundary conditions is discretized at uniform collocation points. Operational matrices are employed to represent the fractional-time derivative, spatial derivatives, and Volterra integral term, thereby reducing the continuous problem to a system of algebraic equations. An upper error bound in the infinity norm and a residual-based error-estimation procedure are also discussed. Numerical examples illustrate the applicability and accuracy of the proposed approach and include comparisons with exact solutions and with results reported in the literature for alternative methods.

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Cite

BibTeXRIS
BibTeX
@article{damirchi2026pelllucas,
  title = {{Pell–Lucas Collocation Method for Time-Fractional Partial Integro-Differential Equations}},
  author = {Javad Damirchi and Ahmadreza Yazdanian and Shohreh Mehranpour and Mahdi Mahmoudi},
  journal = {Mathematics},
  year = {2026},
  month = nov,
  doi = {10.3390/math14213983},
  url = {https://www.mdpi.com/2227-7390/14/21/3983},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Pell–Lucas Collocation Method for Time-Fractional Partial Integro-Differential Equations
AU  - Javad Damirchi
AU  - Ahmadreza Yazdanian
AU  - Shohreh Mehranpour
AU  - Mahdi Mahmoudi
PY  - 2026
DA  - 2026/11/01
JO  - Mathematics
DO  - 10.3390/math14213983
UR  - https://www.mdpi.com/2227-7390/14/21/3983
AB  - This paper presents a Pell–Lucas collocation method for time-fractional partial integro-differential equations (TFPIDEs) with initial and boundary conditions, where the fractional derivative is taken in the Caputo sense. The unknown solution is approximated by a truncated bivariate Pell–Lucas series, and the governing equation together with the initial and boundary conditions is discretized at uniform collocation points. Operational matrices are employed to represent the fractional-time derivative, spatial derivatives, and Volterra integral term, thereby reducing the continuous problem to a system of algebraic equations. An upper error bound in the infinity norm and a residual-based error-estimation procedure are also discussed. Numerical examples illustrate the applicability and accuracy of the proposed approach and include comparisons with exact solutions and with results reported in the literature for alternative methods.
SN  - 2227-7390
ER  -