Approximate controllability of sub-diffusion equation with impulsive condition

Abstract

In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ∈ (0, 1). Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain.