**Lakshman Mahto 1, Syed Abbas 2,\*, Mokhtar Hafayed <sup>3</sup> and Hari M. Srivastava 4,5**


Received: 7 January 2019; Accepted: 14 February 2019; Published: 17 February 2019

**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.

**Keywords:** fractional diffusion equation; controllability; impulsive system; unique continuation property

**MSC:** 93B05; 34A08; 47H10; 49J15; 26A33; 45K05
