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

The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order 0 < alpha <= 2 is used. The investigated equation can be considered as the time-fractional generalization of the bioheat equation and the Klein-Gordon equation. Different formulations of the problem for integer values of the time-derivatives alpha = 1 and alpha = 2 are also discussed. The integral transform technique is employed. The outcomes of numerical calculations are illustrated graphically for different values of the parameters.

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This paper studies the axisymmetric time-fractional diffusion equation with mass absorption using the Caputo derivative. It discusses different formulations of the problem for integer values of the time-derivatives and employs the integral transform technique. The numerical calculations are illustrated graphically for different parameter values.