Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations

Abstract

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be directly measured, which requires one to discuss inverse problems of identifying these physical quantities from some indirectly observed information of solutions. Inverse problems in determining these unknown parameters of the model are not only theoretically interesting, but also necessary for finding solutions to initial-boundary value problems and studying properties of solutions. This chapter surveys works on such inverse problems for fractional diffusion equations.

References in corpus (5)

• Distributed Order Calculus and Equations of Ultraslow Diffusion
• Distributed-order fractional Cauchy problems on bounded domains
• Distributed Order Derivatives and Relaxation Patterns
• Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients
• An inverse problem for distributed order time-fractional diffusion equations

Cited by in corpus (9)

• Determination of the order of fractional derivative for subdiffusion equation
• Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
• Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
• Initial-boundary value problems for coupled systems of time-fractional diffusion equations
• Inverse moving source problem for time-fractional evolution equations: Determination of profiles
• Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation
• Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients
• Recovering Multiple Fractional Orders in Time-Fractional Diffusion in an Unknown Medium
• Regularized Reconstruction of Scalar Parameters in Subdiffusion with Memory via a Nonlocal Observation