SOLUSI NUMERIK PERSAMAAN DIFERENSIAL FRAKSIONAL CAPUTO MENGGUNAKAN POLINOMIAL INTERPOLASI KUADRATIK

Zulkarnain Zulkarnain, Imran M, Khozin Mu’tamar, Supriadi Putra

Abstract


This study investigates the numerical solution of fractional differential equations using the Caputo fractional derivative of order . The proposed method is based on the analytical properties of fractional differential equations, which can be reformulated as nonlinear Volterra integral equations of the second kind. A quadratic polynomial interpolation is employed to approximate the solution of the integral equation. Numerical simulations are conducted to evaluate the accuracy and efficiency of the proposed method and to compare its performance with several existing numerical methods. The numerical simulations indicate that the proposed method performs better than the two benchmark methods over short time intervals, especially when using larger step sizes. This makes it more efficient by reducing the overall computational cost.


Keywords


fractional differential equations, Caputo fractional derivative, Volterra integral equation, quadratic interpolation, numerical method

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DOI: https://doi.org/10.20527/epsilon.v19i1.15269

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