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April 12, 2026Open Access

Fractional Differential Equations (FDEs) In Viscoelasticity Or Anomalous Diffusion

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Authors

JYJitin Yadav

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Overview

Mathematical modeling demonstrates efficient anomalous diffusion behavior, highlighting implications for various systems.

Key Points

  • The aim is to develop a fractional diffusion model that effectively accounts for memory-dependent transport in systems exhibiting anomalous diffusion.
  • Develop a time-fractional diffusion model using the Caputo fractional derivative.
  • Derive a fractional diffusion equation from mass conservation and temporal memory relations.
  • Present an analytical solution using Laplace and Fourier transforms.
  • Construct a numerical approximation via the L1 finite difference scheme.
  • Analyze the stability and convergence properties of the numerical method.
  • The fractional order of the model controls the transition from normal to subdiffusive transport.
  • The model accurately reproduces power-law mean squared displacement behavior.
  • Fractional differential equations require significantly fewer parameters compared to classical multi-scale models.
  • Numerical experiments validate the effectiveness of the model in describing memory-driven diffusion processes.

Cite This Study

Jitin Yadav (2015) studied this question.

synapsesocial.com/papers/69db38534fe01fead37c68ebhttps://doi.org/10.5281/zenodo.19500415
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