Salama, M., Zedan, H., Abd-Elhameed, W., Youssri, Y.. (1405). A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients. , 57(3), 425-442. doi: 10.22059/jcamech.2026.412544.1799
M. H. Salama; H. A. Zedan; W. M. Abd-Elhameed; Y. H. Youssri. "A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients". , 57, 3, 1405, 425-442. doi: 10.22059/jcamech.2026.412544.1799
Salama, M., Zedan, H., Abd-Elhameed, W., Youssri, Y.. (1405). 'A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients', , 57(3), pp. 425-442. doi: 10.22059/jcamech.2026.412544.1799
Salama, M., Zedan, H., Abd-Elhameed, W., Youssri, Y.. A Spectrally Accurate Shifted Lucas Collocation Framework for Fractional Lanchester Combat Dynamics with Time-Dependent Variable Coefficients. , 1405; 57(3): 425-442. doi: 10.22059/jcamech.2026.412544.1799

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

Journal of Computational Applied Mechanics
دوره 57، شماره 3، پاییز 2026، صفحه 425-442    اصل مقاله (1.43 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jcamech.2026.412544.1799
نویسندگان
M. H. Salama1؛ H. A. Zedan1؛ W. M. Abd-Elhameed2؛ Y. H. Youssri* 2، 3، 4
1Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
3Faculty of Engineering, Egypt University of Informatics, Knowledge City, New Administrative Capital 19519, Egypt
4Associate Fellow (AFHEA) of the Higher Education Academy (Advance HE), UK
چکیده
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.
کلیدواژه‌ها
Fractional dynamical systems؛ Spectral collocation؛ Caputo derivative؛ Operational matrix؛ Coupled fractional ODEs؛ Mittag-Leffler stability؛ Numerical methods
مراجع
آمار
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