Basic existence and uniqueness results for solutions to systems of nonlinear fractional differential equations

Tisdell, CC; Liu, Z; MacNamara, S

Basic existence and uniqueness results for solutions to systems of nonlinear fractional differential equations

Tisdell, CC Liu, Z MacNamara, S

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Publication Type:: Journal Article
Citation:: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 2017, 24 (3), pp. 181 - 193
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Tisdell, CC	en_US
dc.contributor.author	Liu, Z	en_US
dc.contributor.author	MacNamara, S	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 2017, 24 (3), pp. 181 - 193	en_US
dc.identifier.issn	1201-3390	en_US
dc.identifier.uri	http://hdl.handle.net/10453/125661
dc.description.abstract	© 2017 Watam Press. We produce new global existence and uniqueness results for solutions to systems of initial value problems involving fractional differential equations. The uniqueness results rely on differential inequalities and a comparison with monotonically converging sequences of functions. The existence results involve fixed-point theorems that rely on a strategic choice of Liapunov function and harness new a priori bounds on solutions. We present an example where the new results yield existence of solutions, but the classical global Cauchy-Lipschitz approach does not directly apply.	en_US
dc.relation.ispartof	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis	en_US
dc.subject.classification	Applied Mathematics	en_US
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	Basic existence and uniqueness results for solutions to systems of nonlinear fractional differential equations	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	24	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	24	en_US

Abstract:

© 2017 Watam Press. We produce new global existence and uniqueness results for solutions to systems of initial value problems involving fractional differential equations. The uniqueness results rely on differential inequalities and a comparison with monotonically converging sequences of functions. The existence results involve fixed-point theorems that rely on a strategic choice of Liapunov function and harness new a priori bounds on solutions. We present an example where the new results yield existence of solutions, but the classical global Cauchy-Lipschitz approach does not directly apply.

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http://hdl.handle.net/10453/125661