Unique Continuation Principle for the One-Dimensional Time-Fractional Diffusion Equation

This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α ∈ (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.