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Saini, Gaurav, Ghosh, Bappa, Chand, Sunita. (1404). An accurate computational approach for solving system of differential equations involving non-local derivatives. فیزیولوژی و بیوتکنولوژی آبزیان, 14(1), 19-34. doi: 10.22124/jmm.2025.30849.2765
Gaurav Saini; Bappa Ghosh; Sunita Chand. "An accurate computational approach for solving system of differential equations involving non-local derivatives". فیزیولوژی و بیوتکنولوژی آبزیان, 14, 1, 1404, 19-34. doi: 10.22124/jmm.2025.30849.2765
Saini, Gaurav, Ghosh, Bappa, Chand, Sunita. (1404). 'An accurate computational approach for solving system of differential equations involving non-local derivatives', فیزیولوژی و بیوتکنولوژی آبزیان, 14(1), pp. 19-34. doi: 10.22124/jmm.2025.30849.2765
Saini, Gaurav, Ghosh, Bappa, Chand, Sunita. An accurate computational approach for solving system of differential equations involving non-local derivatives. فیزیولوژی و بیوتکنولوژی آبزیان, 1404; 14(1): 19-34. doi: 10.22124/jmm.2025.30849.2765

An accurate computational approach for solving system of differential equations involving non-local derivatives

Journal of Mathematical Modeling
دوره 14، شماره 1، خرداد 2026، صفحه 19-34    اصل مقاله (408.04 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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