An asymptotic analytical solution to the problem of two moving boundaries with fractional diffusion in one-dimensional drug release devices. (English) Zbl 1180.82242
Summary: We set up a one-dimensional mathematical model with a Caputo fractional operator of a drug released from a polymeric matrix that can be dissolved into a solvent. A two moving boundaries problem in fractional anomalous diffusion (in time) with order \(\alpha\in(0,1]\) under the assumption that the dissolving boundary can be dissolved slowly is presented in this paper. The two-parameter regular perturbation technique and Fourier and Laplace transform methods are used. A dimensionless asymptotic analytical solution is given in terms of the Wright function.
MSC:
82D60 | Statistical mechanics of polymers |
26A33 | Fractional derivatives and integrals |
44A10 | Laplace transform |
42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |