| Summary: | In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>. 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.
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