An approximation technique for a system of time-fractional differential equations arising in population dynamics

Document Type : Research Article

Authors

1 Department of Mathematics, National Institute of Technology Rourkela, India

2 Department of Mathematics, Konark Institute of Science and Technology, India

3 Department of Mathematics, Utkal University, Bhubaneswar, India

Abstract

In this work, we develop and analyze an approximation technique for the system of time-fractional nonlinear differential equations arising in population dynamics. The fractional of order $ \sigma\in(0,1) $ is taken in the Caputo sense. The proposed technique uses L1 discretization on the uniform mesh to approximate the differential operator. The fractional model is transformed into a system of nonlinear algebraic equations. The generalized Newton-Raphson method is employed to solve the corresponding nonlinear system. A rigorous error estimation is presented. It is shown that the proposed scheme achieved $ (2-\sigma) $ order of accuracy. Lastly, numerical experiment is conducted to demonstrate the validity of the proposed technique.

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References

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Journal of Mathematical Modeling
Volume 13, Issue 3
July 2025
Pages 519-531

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