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Mathematics 2019, 7(2), 190;

Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Department of Science and Humanities, Indian Institute of Information Technology Dharwad, Hubli 580029, India
School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., India
Laboratory of Applied Mathematics, Biskra University, Biskra 07000, Algeria
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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
Full-Text   |   PDF [311 KB, uploaded 25 February 2019]   |  


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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