Attenuated Fractional Wave Equations With Anisotropy.

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.