On time-fractional diffusion equations with space-dependent variable order

Abstract

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other coefficients of these equations, by the knowledge of a suitable time-sequence of partial Dirichlet-to-Neumann maps.

References in corpus (8)

• Distributed Order Calculus and Equations of Ultraslow Diffusion
• Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
• A Parabolic Problem with a Fractional-Time Derivative
• Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients
• Uniqueness in inverse boundary value problems for fractional diffusion equations
• Subdiffusive master equation with space dependent anomalous exponent: `Black Swan' effects
• Semi-Markov models and motion in heterogeneous media
• Initial-boundary value problem for distributed order time-fractional diffusion equations

Cited by in corpus (11)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Reconstruction and stable recovery of source terms and coefficients appearing in diffusion equations
• Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
• Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
• On time-fractional partial differential equations of time-dependent piecewise constant order
• On the Rothe-Galerkin spectral discretisation for a class of variable fractional-order nonlinear wave equations
• Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement
• Strong uniqueness principle for fractional polyharmonic operators and applications to inverse problems
• Asymptotic estimates of solutions to time-fractional diffusion equations with space-dependent variable order
• Recovering Multiple Fractional Orders in Time-Fractional Diffusion in an Unknown Medium
• Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations