Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

Abstract

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion Laplace transforms, it turns out that the decay rate of the solution for long time is dominated by the lowest order of the time-fractional derivatives. Finally, as an application of the analyticity of the solution, the uniqueness of an inverse problem in determining the fractional orders in the multi-term time-fractional diffusion equations from one interior point observation is established.

References in corpus (1)

• Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients

Cited by in corpus (5)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations
• Initial-boundary value problems to semilinear multi-term fractional differential equations
• Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative
• Strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations