On the approximate controllability for fractional evolution inclusions of Sobolev and Clarke subdifferential type

Xianghu Liu; Jin Rong Wang; D. O'Regan

doi:10.1093/imamci/dnx031

On the approximate controllability for fractional evolution inclusions of Sobolev and Clarke subdifferential type

Xianghu Liu, Jin Rong Wang, D. O'Regan

Mathematics

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15 Citations (Scopus)

Abstract

This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	IMA Journal of Mathematical Control and Information
Volume	36
Issue number	1
DOIs	https://doi.org/10.1093/imamci/dnx031
Publication status	Published - 22 Mar 2019

Keywords

Caputo fractional derivative
approximate controllability
generalized Clarke subdifferential
hemivariational inequalities
mild solutions

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Liu, XH;Wang, JR;O'Regan, D

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10.1093/imamci/dnx031

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abstract = "This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory.",

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PY - 2019/3/22

Y1 - 2019/3/22

N2 - This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory.

AB - This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory.

KW - Caputo fractional derivative

KW - approximate controllability

KW - generalized Clarke subdifferential

KW - hemivariational inequalities

KW - mild solutions

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JF - IMA Journal of Mathematical Control and Information

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ER -

On the approximate controllability for fractional evolution inclusions of Sobolev and Clarke subdifferential type

Abstract

Keywords

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