Initial-boundary value problem for the time-fractional degenerate diffusion equation

Abstract

In this paper the initial-boundary value problems for the one-dimensional linear time-fractional diffusion equations with the time-fractional derivative ∂ α t of order α ∈ (0, 1) in the variable t and time-degenerate diffusive coefficients t β with β ≥ 1 − α are studied. The solutions of initialboundary value problems for the one-dimensional time-fractional degenerate diffusion equations with the time-fractional derivative ∂ α t of order α ∈ (0, 1) in the variable t, are shown. The second section present Dirichlet and Neumann boundary value problems, and in the third section has shown the solutions of the Dirichlet and Neumann boundary value problem for the one-dimensional linear time-fractional diffusion equation. The solutions of these fractional diffusive equations are presented using the Kilbas-Saigo function Eα,m,l(z). The solution of the problems is discovered by the method of separation of variables, through finding two problems with one variable. The existence and uniqueness to the solution of the problem are confirmed. In addition, the convergence of the solution has been proven using the estimate for the Kilbas-Saigo function Eα,m,l(z) from [13] and Parseval’s identity