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

Abstract

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<α≤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 α=1 and α=2 are also discussed. The integral transform technique is employed. The outcomes of numerical calculations are illustrated graphically for different values of the parameters.

Fractional Heat Conduction with Heat Absorption in a Solid with a Spherical Cavity under Time-Harmonic Heat Flux

“…Graphical representations of numerical simulation results are presented for typical values of the parameters. The present investigation extends and evolves the results of previous studies [37][38][39][40].…”

“…Figure 6 shows the real parts of solutions (71) and (78) taking the non-dimensional quantities (40) for α = 2. -the general solution describing the transition process; -the quasi-steady-state approach (71).…”