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Peer-reviewedCC BYFractal and Fractional

Highly Accurate Galerkin Approach for Modified Anomalous Time-Fractional Sub-Diffusion Equations Based on Fibonacci Coefficient Polynomials

  • Mohamed Adel1
  • Waleed Mohamed Abd-Elhameed2
  • Naher Mohammed A. Alsafri3
  • M. A. El-Naggar4,5
  • Ahmed Gamal Atta6
6 affiliations
  1. 1Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42351, Saudi Arabia
  2. 2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  3. 3Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia
  4. 4Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt
  5. 5Department of General Subjects, University of Business and Technology, Jeddah 21361, Saudi Arabia
  6. 6Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
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Abstract

A spectral Galerkin algorithm is developed for the numerical treatment of modified anomalous time-fractional sub-diffusion equations (MATFSDEs). The algorithm is constructed using Fibonacci coefficient polynomials, from which two space–time trial families are formed. These families are selected so that the homogeneous initial and boundary conditions are automatically incorporated after a suitable transformation of the original problem. The Galerkin formulation then reduces the model to a finite algebraic matrix system whose entries can be explicitly evaluated. To support the construction, inversion, moment, and linearization identities for the selected polynomials are obtained and then used to express the required matrices in closed form. The convergence of the expansion is investigated, and explicit error bounds are derived. Numerical tests are reported to demonstrate the accuracy, applicability, and competitiveness of the proposed scheme in comparison with some existing methods in the literature.

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Cite

BibTeXRIS
BibTeX
@article{adel2026highly,
  title = {{Highly Accurate Galerkin Approach for Modified Anomalous Time-Fractional Sub-Diffusion Equations Based on Fibonacci Coefficient Polynomials}},
  author = {Mohamed Adel and Waleed Mohamed Abd-Elhameed and Naher Mohammed A. Alsafri and M. A. El-Naggar and Ahmed Gamal Atta},
  journal = {Fractal and Fractional},
  year = {2026},
  month = jul,
  doi = {10.3390/fractalfract10080514},
  url = {https://doi.org/10.3390/fractalfract10080514},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Highly Accurate Galerkin Approach for Modified Anomalous Time-Fractional Sub-Diffusion Equations Based on Fibonacci Coefficient Polynomials
AU  - Mohamed Adel
AU  - Waleed Mohamed Abd-Elhameed
AU  - Naher Mohammed A. Alsafri
AU  - M. A. El-Naggar
AU  - Ahmed Gamal Atta
PY  - 2026
DA  - 2026/07/28
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10080514
UR  - https://doi.org/10.3390/fractalfract10080514
AB  - A spectral Galerkin algorithm is developed for the numerical treatment of modified anomalous time-fractional sub-diffusion equations (MATFSDEs). The algorithm is constructed using Fibonacci coefficient polynomials, from which two space–time trial families are formed. These families are selected so that the homogeneous initial and boundary conditions are automatically incorporated after a suitable transformation of the original problem. The Galerkin formulation then reduces the model to a finite algebraic matrix system whose entries can be explicitly evaluated. To support the construction, inversion, moment, and linearization identities for the selected polynomials are obtained and then used to express the required matrices in closed form. The convergence of the expansion is investigated, and explicit error bounds are derived. Numerical tests are reported to demonstrate the accuracy, applicability, and competitiveness of the proposed scheme in comparison with some existing methods in the literature.
SN  - 2504-3110
ER  -