The proposed approach demonstrates reduced errors in solutions of time-fractional advection–diffusion equations, indicating efficiency of the differential evolution optimization technique.
In this study, we introduce an operational matrix (OM) method based on Haar wavelets (HWs) to approximate the solution of time-fractional advection–diffusion equations (TFADEs). These problems involve fractional derivatives in the Atangana–Baleanu Caputo sense. The method employs an OM and a truncated HW series to transform TFADEs into objective functions. Differential evolution optimization was then applied to minimize these objective functions to determine the unknown Haar coefficients. The applicability and efficiency of the proposed method are demonstrated using illustrative examples. The accuracy of the proposed method was verified by comparing its results with those of exact solutions. Furthermore, the performance measures included the mean absolute deviation, root mean square error, Nash–Sutcliffe efficiency, and maximum absolute error, confirming the efficacy and precision of the proposed method.
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Alam et al. (2025) studied this question.
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