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Fractional-order models of species interaction: solitary wave and analytical dynamics | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 مرداد 1405 اصل مقاله (4.08 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.32115.2902 | ||
| نویسندگان | ||
| Hamid Mesgarani* 1؛ Fateme Ahmadi Ghavibazoo2؛ Morteza Garshasbi3 | ||
| 1S‎hahid Rajaee Teacher Training University‎, ‎Tehran‎, ‎Iran‎ | ||
| 2Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 -136, I. R. Iran | ||
| 3School of Mathematics \& Computer Sciences, Iran University of Science \& Technology, Tehran, Iran | ||
| چکیده | ||
| We derive explicit traveling-wave and solitary-wave solutions for a coupled fractional reaction--diffusion system describing interacting populations. The analytical framework combines a rational--exponential ansatz with an auxiliary-function expansion, where the auxiliary function satisfies a linear second-order ordinary differential equation. Time- and space-fractional derivatives, defined in the sense of Jumarie's modified Riemann--Liouville derivative, are incorporated through a fractional complex transformation that reduces the governing fractional partial differential system to an ordinary differential system. A homogeneous-balance procedure yields algebraic relations whose solutions generate several families of closed-form expressions, including hyperbolic, rational, and oscillatory wave profiles classified according to the discriminant of the auxiliary equation. The obtained solutions demonstrate how the fractional-order parameters influence wave propagation, localization, and diffusion behavior, providing additional insight beyond the corresponding classical integer-order model. Representative graphical illustrations together with symbolic verification confirm the validity of the analytical solutions and demonstrate the applicability of the proposed framework for studying nonlinear fractional reaction--diffusion systems. | ||
| کلیدواژهها | ||
| Fractional differential equations؛ Soliton solutions؛ Traveling waves؛ Reaction–diffusion؛ Variable-order fractional derivatives | ||
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