On the nonexistence of blowing-up solutions to a fractional functional-differential equation

Mokhtar Kirane; Milan Medved'; Nasser Eddine Tatar

doi:10.1515/gmj-2012-0006

On the nonexistence of blowing-up solutions to a fractional functional-differential equation

Mokhtar Kirane^*
, Milan Medved'
, Nasser Eddine Tatar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

A sufficient condition for the nonexistence of blowing-up mild solutions of a nonlinear evolution fractional functional-differential equation associated with a strongly continuous semigroup and with a nonlinearity containing the RiemannLiouville fractional integral is established. We prove a result on a new type of nonlinear integral inequalities with weakly singular kernels and delay and apply it in the proof of the result on the nonexistence of blowing-up solutions. This result is applied to a fractionally damped pendulum equation with a time delay forcing term (a feedback control).

Original language	English
Pages (from-to)	127-144
Number of pages	18
Journal	Georgian Mathematical Journal
Volume	19
Issue number	1
DOIs	https://doi.org/10.1515/gmj-2012-0006
State	Published - Mar 2012

Bibliographical note

Funding Information:
The work of the second author was supported by the Slovak Research and Development Agency under the contracts No. APVV-0134-10and by the Slovak Grant Agency VEGA-MS, No. 1/0507/11. The third author is very grateful for the financial support of King Fahd University of Petroleum and Minerals.

Keywords

Blowing-up solution
Functional-differential equation
HenryGronwall inequality
RiemannLiouville fractional integral

ASJC Scopus subject areas

General Mathematics

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title = "On the nonexistence of blowing-up solutions to a fractional functional-differential equation",

abstract = "A sufficient condition for the nonexistence of blowing-up mild solutions of a nonlinear evolution fractional functional-differential equation associated with a strongly continuous semigroup and with a nonlinearity containing the RiemannLiouville fractional integral is established. We prove a result on a new type of nonlinear integral inequalities with weakly singular kernels and delay and apply it in the proof of the result on the nonexistence of blowing-up solutions. This result is applied to a fractionally damped pendulum equation with a time delay forcing term (a feedback control).",

keywords = "Blowing-up solution, Functional-differential equation, HenryGronwall inequality, RiemannLiouville fractional integral",

author = "Mokhtar Kirane and Milan Medved' and Tatar, \{Nasser Eddine\}",

note = "Funding Information: The work of the second author was supported by the Slovak Research and Development Agency under the contracts No. APVV-0134-10and by the Slovak Grant Agency VEGA-MS, No. 1/0507/11. The third author is very grateful for the financial support of King Fahd University of Petroleum and Minerals.",

year = "2012",

month = mar,

doi = "10.1515/gmj-2012-0006",

language = "English",

volume = "19",

pages = "127--144",

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AU - Kirane, Mokhtar

AU - Medved', Milan

AU - Tatar, Nasser Eddine

N1 - Funding Information: The work of the second author was supported by the Slovak Research and Development Agency under the contracts No. APVV-0134-10and by the Slovak Grant Agency VEGA-MS, No. 1/0507/11. The third author is very grateful for the financial support of King Fahd University of Petroleum and Minerals.

PY - 2012/3

Y1 - 2012/3

N2 - A sufficient condition for the nonexistence of blowing-up mild solutions of a nonlinear evolution fractional functional-differential equation associated with a strongly continuous semigroup and with a nonlinearity containing the RiemannLiouville fractional integral is established. We prove a result on a new type of nonlinear integral inequalities with weakly singular kernels and delay and apply it in the proof of the result on the nonexistence of blowing-up solutions. This result is applied to a fractionally damped pendulum equation with a time delay forcing term (a feedback control).

AB - A sufficient condition for the nonexistence of blowing-up mild solutions of a nonlinear evolution fractional functional-differential equation associated with a strongly continuous semigroup and with a nonlinearity containing the RiemannLiouville fractional integral is established. We prove a result on a new type of nonlinear integral inequalities with weakly singular kernels and delay and apply it in the proof of the result on the nonexistence of blowing-up solutions. This result is applied to a fractionally damped pendulum equation with a time delay forcing term (a feedback control).

KW - Blowing-up solution

KW - Functional-differential equation

KW - HenryGronwall inequality

KW - RiemannLiouville fractional integral

UR - https://www.scopus.com/pages/publications/84860539372

U2 - 10.1515/gmj-2012-0006

DO - 10.1515/gmj-2012-0006

M3 - Article

AN - SCOPUS:84860539372

SN - 1572-9176

VL - 19

SP - 127

EP - 144

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 1

ER -

On the nonexistence of blowing-up solutions to a fractional functional-differential equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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