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An accurate computational approach for solving system of differential equations involving non-local derivatives | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 08 شهریور 1404 اصل مقاله (408.73 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.30849.2765 | ||
| نویسندگان | ||
| Gaurav Saini1؛ Bappa Ghosh* 2؛ Sunita Chand3 | ||
| 1Assistant Professor Center for Data Science, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University) | ||
| 2Assistant Professor Center for Artificial Intelligence and Machine Learning Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University) | ||
| 3Professor Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University) | ||
| چکیده | ||
| This paper addresses the numerical approximation of a system of differential equations involving fractional derivatives of arbitrary order. The derivatives are governed in the Caputo sense of orders $\alpha_i \in(0,1)$. Motivated by the complexity of modeling coupled fractional dynamics, an efficient numerical scheme based on the classical L1 discretization technique is developed. The proposed method effectively captures the behavior of the system across various fractional orders and parameter regimes. A rigorous convergence analysis confirms the consistency of the proposed technique and establishes a convergence rate of order $\min_{p}\{2 - \alpha_p\}$. Numerical experiments are conducted to validate the theoretical findings, demonstrating excellent agreement with exact solutions and confirming the computational efficiency of the approach. These results highlight the robustness of the proposed scheme for solving the differential system with memory effects. | ||
| کلیدواژه‌ها | ||
| System of differential equations؛ Caputo derivative؛ L1 scheme؛ convergence analysis | ||
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آمار تعداد مشاهده مقاله: 37 تعداد دریافت فایل اصل مقاله: 42 |
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