Journal of Computational Applied Mechanics

A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

2 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

3 Faculty of Engineering, Egypt University of Informatics, Knowledge City, New Administrative Capital 19519, Egypt

4 Associate Fellow (AFHEA) of the Higher Education Academy (Advance HE), UK

Abstract

This paper is confined to developing a rigorous computational framework using the shifted Lucas polynomials for the numerical treatment of the generalized fractional-order Lanchester combat model characterized by time-dependent variable coefficients. The method uses an exact operational matrix for the Caputo derivative to handle the singular kernel, thereby eliminating the need for numerical quadrature. A global polynomial projection at shifted Chebyshev–Gauss–Lobatto nodes eliminates predictor–corrector errors and preserves high-order accuracy under memory effects. A rigorous analysis employing a generalized Gronwall inequality establishes well-posedness and derives sharp stability bounds via Mittag–Leffler functions. Numerical investigations validate enhanced stability and efficiency, especially for memory effects and heavy-tail decay, and error estimates indicate super-geometric convergence.

Keywords

Main Subjects

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Journal of Computational Applied Mechanics
Volume 57, Issue 3
July 2026
Pages 425-442
  • Receive Date: 10 April 2026
  • Accept Date: 12 April 2026