Iterative Learning Control for Nonlinear Pantograph Systems with Hilfer Fractional Derivatives

Authors

  • Abdulah Alghamdi Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia https://orcid.org/0000-0002-8636-1960
  • D. Vivek Department of Mathematics, PSG College of Arts & Science, Coimbatore-641014, India.
  • S. Sunmitha Department of Mathematics, PSG College of Arts & Science, Coimbatore-641014, India. https://orcid.org/0009-0006-3518-1915
  • E. M. Elsayed Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. https://orcid.org/0000-0003-0894-8472
  • M. M. El-Dessoky Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia. https://orcid.org/0000-0001-8934-2442

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7130

Keywords:

Hilfer fractional derivative; Pantograph equation; Gronwall inequality; Iterative learning control; Convergent.

Abstract

This paper investigates the trajectory tracking problem for nonlinear pantograph systems governed by the Hilfer fractional derivative. The presence of fractional memory and proportional delay significantly complicates the control design. To address this issue, P-type and D-type iterative learning control laws are developed to progressively improve the tracking performance over repeated iterations. Additionally, the (1 − γ, λ)-weighted norm is used for the robust convergence of the suggested control techniques. Finally, a numerical example illustrates the effectiveness of the proposed control strategies.

References

Downloads

Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Differential Equations

License

Copyright (c) 2026 Abdulah Alghamdi, D. Vivek, S. Sunmitha, E. M. Elsayed, M. M. El-Dessoky

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Iterative Learning Control for Nonlinear Pantograph Systems with Hilfer Fractional Derivatives. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7130. https://doi.org/10.29020/nybg.ejpam.v19i2.7130