ON THE OSCILLATION OF THREE DIMENSIONAL alpha-FRACTIONAL DIFFERENTIAL SYSTEMS

TitleON THE OSCILLATION OF THREE DIMENSIONAL alpha-FRACTIONAL DIFFERENTIAL SYSTEMS
Publication TypeJournal Article
Year of Publication2018
AuthorsCHATZARAKIS G.E., DEEPA M., NAGAJOTHI N., SADHASIVAM V.
JournalDynamic Systems and Applications
Volume27
Issue4
Start Page873
Pagination22
Date Published11/2018
ISSN1056-2176
AMS Subject Classification34A08, 34A34, 34K11
Abstract

In this article, we consider the three dimensional $\alpha$-fractional nonlinear differential system of the form $$ D^{\alpha}\left(x(t)\right)=a(t)f\left(y(t)\right), $$ $$ D^{\alpha}\left(y(t)\right)=-b(t)g\left(z(t)\right), $$ $$ D^{\alpha}\left(z(t)\right)=c(t)h\left(x(t)\right),\quad t \geq t_0, $$ where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We establish some new sufficient conditions for the oscillation of the solutions of the differential system, using the generalized Riccati transformation and inequality technique. Examples illustrating the results are also given.

PDFhttps://acadsol.eu/dsa/articles/27/4/12.pdf
DOI10.12732/dsa.v27i4.12
Refereed DesignationRefereed
Full Text

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