فهرست نشریات علمی دسترسی آزاد ایران

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.