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We use Sadavoskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order α ∈ (0, 1) with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

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.

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