$On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay$
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On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay

In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other...

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Main Authors:	Yuxin Zhang, Xiping Liu, Mei Jia
Format:	article
Language:	EN
Published:	Vilnius University Press 2021
Subjects:	boundary value problem piecewise differential equation left and right fractional derivative delay disturbance parameter fixed point theorem Analysis QA299.6-433
Online Access:	https://doaj.org/article/89b936ca13ae42dcad765ce64a5a13fb
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spelling	oai:doaj.org-article:89b936ca13ae42dcad765ce64a5a13fb2021-12-02T19:40:39ZOn the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay10.15388/namc.2021.26.246221392-51132335-8963https://doaj.org/article/89b936ca13ae42dcad765ce64a5a13fb2021-11-01T00:00:00Zhttps://www.journals.vu.lt/nonlinear-analysis/article/view/24622https://doaj.org/toc/1392-5113https://doaj.org/toc/2335-8963 In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results. Yuxin ZhangXiping LiuMei JiaVilnius University Pressarticleboundary value problempiecewise differential equationleft and right fractional derivativedelaydisturbance parameterfixed point theoremAnalysisQA299.6-433ENNonlinear Analysis, Vol 26, Iss 6 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	boundary value problem piecewise differential equation left and right fractional derivative delay disturbance parameter fixed point theorem Analysis QA299.6-433
spellingShingle	boundary value problem piecewise differential equation left and right fractional derivative delay disturbance parameter fixed point theorem Analysis QA299.6-433 Yuxin Zhang Xiping Liu Mei Jia On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
description	In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results.
format	article
author	Yuxin Zhang Xiping Liu Mei Jia
author_facet	Yuxin Zhang Xiping Liu Mei Jia
author_sort	Yuxin Zhang
title	On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
title_short	On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
title_full	On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
title_fullStr	On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
title_full_unstemmed	On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
title_sort	on the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay
publisher	Vilnius University Press
publishDate	2021
url	https://doaj.org/article/89b936ca13ae42dcad765ce64a5a13fb
work_keys_str_mv	AT yuxinzhang ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay AT xipingliu ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay AT meijia ontheboundaryvalueproblemsofpiecewisedifferentialequationswithleftrightfractionalderivativesanddelay
_version_	1718376213543649280

On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay

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