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October 2, 2025Mathematical Methods in the Applied Sciences

Capturing Nonlocal Effects in Fractional Dynamics: Riesz Derivatives as a New Frontier in Modeling Complex Diffusion and Pattern Formation

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Authors

MAManal AlqhtaniKOKolade M. OwolabiKSKhaled M. Saad

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Overview

This research reveals the impact of the Riesz derivative on fractional dynamics and nonlocal effects in system behavior.

Key Points

  • The proposed numerical method shows effectiveness in modeling anomalous diffusion phenomena.
  • A high-order approximation scheme combines left- and right-sided derivatives providing enhanced stability.
  • The Riesz derivative framework captures nonlocal effects in complex dynamics of fractional equations.
  • Experimental results demonstrate intricate behaviors of pattern formation under varying fractional parameters.

Cite This Study

Alqhtani et al. (2025) studied this question.

synapsesocial.com/papers/68de84b65b556a9128e1b656https://doi.org/10.1002/mma.70120
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