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

Document Type : Research Article

Authors

1 Center for Data Science, Department of Computer Science and Engineering, Siksha ‘O’ Anusandhan (Deemed to be University), India

2 Center for Artificial Intelligence and Machine Learning, Department of Computer Science and Engineering, Siksha ‘O’ Anusandhan (Deemed to be University), India

3 Department of Mathematics, Siksha ‘O’ Anusandhan (Deemed to be University), India

Abstract

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.

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References

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Journal of Mathematical Modeling
Volume 14, Issue 1
March 2026
Pages 19-34

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