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

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(۰,۱). Motivated by the complexity of modeling coupled fractional dynamics, an efficient numerical scheme based on the classical L۱ 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}\{۲ - \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.

کلیدواژه ها:

System of differential equations ، Caputo derivative ، L۱ scheme ، convergence Analysis