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Attenuated Fractional Wave Equations With Anisotropy.

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New fractional calculus models capture anisotropic wave propagation by allowing different attenuation in each coordinate. This approach models power law attenuation and anomalous dispersion for complex media analysis.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Geophysics

Background:

  • Wave propagation in complex media often exhibits anisotropic behavior.
  • Existing models may not fully capture directional variations in attenuation and dispersion.
  • Fractional calculus offers a powerful framework for modeling complex physical phenomena.

Purpose of the Study:

  • To develop novel fractional calculus models for wave propagation.
  • To incorporate anisotropic attenuation characteristics into wave propagation models.
  • To provide analytical expressions for power law attenuation and anomalous dispersion.

Main Methods:

  • Development of fractional calculus equations tailored for wave propagation.
  • Inclusion of coordinate-dependent attenuation indices.
  • Derivation of analytical solutions for power law attenuation and anomalous dispersion.

Main Results:

  • Successfully developed fractional calculus models for anisotropic wave propagation.
  • Demonstrated the ability to represent distinct attenuation indices per coordinate.
  • Derived analytical expressions for power law attenuation and anomalous dispersion in each direction.

Conclusions:

  • The proposed fractional calculus models effectively capture anisotropic wave propagation.
  • These models offer a more comprehensive understanding of wave behavior in complex media.
  • The derived analytical expressions are valuable for analyzing power law attenuation and anomalous dispersion.