Unique continuation principle for the one-dimensional time-fractional diffusion equation

Abstract

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order $\alpha \in (0,1)$. Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

References in corpus (1)

• Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients

Cited by in corpus (2)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations