Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Lakshman Mahto, Syed Abbas, Mokhtar Hafayed and Hari M. Srivastava
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Lakshman Mahto: Department of Science and Humanities, Indian Institute of Information Technology Dharwad, Hubli 580029, India
Syed Abbas: School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., India
Mokhtar Hafayed: Laboratory of Applied Mathematics, Biskra University, Biskra 07000, Algeria
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

Mathematics, 2019, vol. 7, issue 2, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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