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Analysis and numerical approximation for space-dependent variable-order fractional diffusion equation in the flowing media

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Analysis reveals convergence rates for a variable-order fractional diffusion equation in flowing media, highlighting numerical methods for accuracy.

The proposed method achieves an Oτ convergence rate, demonstrating its effectiveness in approximating the solution.
Regularity estimates are derived under specified conditions on the velocity field and variable-order, ensuring solution stability.
Finite element methods are employed to approximate spatial operators effectively, maintaining optimal spatial error estimates.
Numerical examples validate the theoretical results, confirming the method's utility in practical applications.

Nie et al. (2025) studied this question.

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Analysis reveals convergence rates for a variable-order fractional diffusion equation in flowing media, highlighting numerical methods for accuracy.