Skip to content
DraconiticResearch
Search Sources API
194,164 studies31 sourcesUpdated 33 min ago
Peer-reviewedCC BYFractal and Fractional

Shifted Pell–Lucas Polynomial-Based Algorithms for Fractional and Classical Rosenau–Hyman Models

  • Waleed Mohamed Abd-Elhameed1
  • Hassan M. Alshehri2
  • Mohammed H. Alharbi2
  • Omar Mazen Alqubori2
  • Amr Kamel Amin3
  • Ahmed Gamal Atta4
4 affiliations
  1. 1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  2. 2Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia
  3. 3Department of Mathematics, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia
  4. 4Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
Open at sourceDOICite

Abstract

This paper introduces two numerical algorithms for solving the fractional and classical Rosenau–Hyman equations. Certain shifted Pell–Lucas polynomials (SPLPs) are employed. New formulas for these polynomials are developed and used to analyze our proposed algorithms, together with the application of the typical collocation method. The established operational matrices for both integer and fractional derivatives are used to convert the problems, along with their governing conditions, into matrix systems that can be treated effectively. The convergence of the shifted Pell–Lucas expansion is thoroughly investigated by developing new estimates. The high accuracy and efficiency of the proposed numerical algorithms are tested through numerical experiments supported by comparisons with some other techniques in the literature.

Related

  1. A Shifted One-Parameter Horadam Polynomial Framework for the Time-Fractional Supergeneralized Viscous Burgers Equation
    Waleed Mohamed Abd-Elhameed, Hussam Salah Alahmadi, Omar Mazen Alqubori +3
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  2. A Shifted Balanced Polynomial Collocation Framework for Variable-Coefficient Multi-Term Time-Fractional Convection–Diffusion–Reaction Problems
    Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Naher Mohammed A. Alsafri +3
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  3. Polynomial-time classical algorithms for mean-field models up to the glass transition
    Alexander Schmidhuber, Alexander Zlokapa
    arXivPreprintarXiv licenceFull textMathematical physicsCondensed matterarXiv
  4. A high-order polynomial-corrected shifted boundary method for simulating fully nonlinear water waves
    Jens Visbech, Allan P. Engsig-Karup, Harry B. Bingham +1
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingFluid dynamicsarXiv
  5. Shifted poles and chamber cancellation for classical Witten zeta functions
    Jonas Matuzas
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@article{abdelhameed2026shifted,
  title = {{Shifted Pell–Lucas Polynomial-Based Algorithms for Fractional and Classical Rosenau–Hyman Models}},
  author = {Waleed Mohamed Abd-Elhameed and Hassan M. Alshehri and Mohammed H. Alharbi and Omar Mazen Alqubori and Amr Kamel Amin and Ahmed Gamal Atta},
  journal = {Fractal and Fractional},
  year = {2026},
  month = may,
  doi = {10.3390/fractalfract10060359},
  url = {https://doi.org/10.3390/fractalfract10060359},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Shifted Pell–Lucas Polynomial-Based Algorithms for Fractional and Classical Rosenau–Hyman Models
AU  - Waleed Mohamed Abd-Elhameed
AU  - Hassan M. Alshehri
AU  - Mohammed H. Alharbi
AU  - Omar Mazen Alqubori
AU  - Amr Kamel Amin
AU  - Ahmed Gamal Atta
PY  - 2026
DA  - 2026/05/26
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10060359
UR  - https://doi.org/10.3390/fractalfract10060359
AB  - This paper introduces two numerical algorithms for solving the fractional and classical Rosenau–Hyman equations. Certain shifted Pell–Lucas polynomials (SPLPs) are employed. New formulas for these polynomials are developed and used to analyze our proposed algorithms, together with the application of the typical collocation method. The established operational matrices for both integer and fractional derivatives are used to convert the problems, along with their governing conditions, into matrix systems that can be treated effectively. The convergence of the shifted Pell–Lucas expansion is thoroughly investigated by developing new estimates. The high accuracy and efficiency of the proposed numerical algorithms are tested through numerical experiments supported by comparisons with some other techniques in the literature.
SN  - 2504-3110
ER  -