University of Tehran Press Journal of Computational Applied Mechanics 2423-6713 57 3 2026 06 01 A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients 425 442 106519 10.22059/jcamech.2026.412544.1799 EN M. H. Salama Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt 0009-0007-7248-6459 H. A. Zedan Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt 0000-0001-6124-9190 W. M. Abd-Elhameed Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt 0000-0002-6102-671X Y. H. Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt Faculty of Engineering, Egypt University of Informatics, Knowledge City, New Administrative Capital 19519, Egypt Associate Fellow (AFHEA) of the Higher Education Academy (Advance HE), UK 0000-0003-0403-8797 Journal Article 2026 04 10 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. https://jcamech.ut.ac.ir/article_106519_fd75ed529c0639753ea8f0845c9423a4.pdf