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Mathematics 2019, 7(2), 190; https://doi.org/10.3390/math7020190

Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

1
Department of Science and Humanities, Indian Institute of Information Technology Dharwad, Hubli 580029, India
2
School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., India
3
Laboratory of Applied Mathematics, Biskra University, Biskra 07000, Algeria
4
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
5
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Received: 7 January 2019 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 17 February 2019
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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. View Full-Text
Keywords: fractional diffusion equation; controllability; impulsive system; unique continuation property fractional diffusion equation; controllability; impulsive system; unique continuation property
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Mahto, L.; Abbas, S.; Hafayed, M.; Srivastava, H.M. Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition. Mathematics 2019, 7, 190.

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