Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

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>&#945;</mi> <mo>&#8712;</mo> <mo stretchy="false">(...

Full description

Bibliographic Details
Main Authors: Lakshman Mahto, Syed Abbas, Mokhtar Hafayed, Hari M. Srivastava
Format: Article
Language:English
Published: MDPI AG 2019-02-01
Series:Mathematics
Subjects:
fractional diffusion equation
controllability
impulsive system
unique continuation property
Online Access:https://www.mdpi.com/2227-7390/7/2/190
id doaj-3946597c666642d8b67d79d1049f0b6e
record_format Article
spelling doaj-3946597c666642d8b67d79d1049f0b6e2020-11-25T02:11:08ZengMDPI AGMathematics2227-73902019-02-017219010.3390/math7020190math7020190Approximate Controllability of Sub-Diffusion Equation with Impulsive ConditionLakshman Mahto0Syed Abbas1Mokhtar Hafayed2Hari M. Srivastava3Department of Science and Humanities, Indian Institute of Information Technology Dharwad, Hubli 580029, IndiaSchool of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., IndiaLaboratory of Applied Mathematics, Biskra University, Biskra 07000, AlgeriaDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaIn this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#945;</mi> <mo>&#8712;</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.https://www.mdpi.com/2227-7390/7/2/190fractional diffusion equationcontrollabilityimpulsive systemunique continuation property
collection DOAJ
language English
format Article
sources DOAJ
author Lakshman Mahto
Syed Abbas
Mokhtar Hafayed
Hari M. Srivastava
spellingShingle Lakshman Mahto
Syed Abbas
Mokhtar Hafayed
Hari M. Srivastava
Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
Mathematics
fractional diffusion equation
controllability
impulsive system
unique continuation property
author_facet Lakshman Mahto
Syed Abbas
Mokhtar Hafayed
Hari M. Srivastava
author_sort Lakshman Mahto
title Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
title_short Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
title_full Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
title_fullStr Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
title_full_unstemmed Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
title_sort approximate controllability of sub-diffusion equation with impulsive condition
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-02-01
description 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>&#945;</mi> <mo>&#8712;</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.
topic fractional diffusion equation
controllability
impulsive system
unique continuation property
url https://www.mdpi.com/2227-7390/7/2/190
work_keys_str_mv AT lakshmanmahto approximatecontrollabilityofsubdiffusionequationwithimpulsivecondition
AT syedabbas approximatecontrollabilityofsubdiffusionequationwithimpulsivecondition
AT mokhtarhafayed approximatecontrollabilityofsubdiffusionequationwithimpulsivecondition
AT harimsrivastava approximatecontrollabilityofsubdiffusionequationwithimpulsivecondition
_version_ 1724916154339688448

Similar Items