Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact

Area of Science:

• Mathematical Physics
• Applied Mathematics
• Fractional Calculus

Background:

• The study addresses the axisymmetric time-fractional diffusion equation with mass absorption.
• It utilizes the Caputo derivative, generalizing bioheat and Klein-Gordon equations.

Purpose of the Study:

• To investigate the axisymmetric time-fractional diffusion equation with mass absorption in a circular domain.
• To analyze the behavior of the system under time-harmonic Dirichlet boundary conditions.
• To explore formulations for integer time-derivative orders (α=1, α=2).

Main Methods:

• Application of the integral transform technique.
• Numerical calculations and graphical illustrations of results.
• Analysis of the Caputo fractional derivative of order 0<α≤2.

Main Results:

• Solutions for the time-fractional diffusion equation with mass absorption were obtained.
• The influence of different parameter values on the system's behavior was demonstrated graphically.
• Comparison with integer-order derivative formulations was discussed.

Conclusions:

• The integral transform technique is effective for solving this class of fractional partial differential equations.
• The study provides a framework for understanding fractional diffusion phenomena with mass absorption.
• Graphical results offer valuable insights for applications in various scientific fields.