An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient

This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under co...
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Autor*in:	B.I. Efendiev [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality

Übergeordnetes Werk:	In: Қарағанды университетінің хабаршысы. Математика сериясы - Academician Ye.A. Buketov Karaganda University, 2023, 106(2022), 2
Übergeordnetes Werk:	volume:106 ; year:2022 ; number:2

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.31489/2022m2/83-92

Katalog-ID:	DOAJ09799359X

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allfields	10.31489/2022m2/83-92 doi (DE-627)DOAJ09799359X (DE-599)DOAJdef66c345cf54be482673999440c8f7c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 B.I. Efendiev verfasserin aut An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found. fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality Analysis Analytic mechanics Probabilities. Mathematical statistics In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 106(2022), 2 (DE-627)DOAJ00015783X 26635011 nnns volume:106 year:2022 number:2 https://doi.org/10.31489/2022m2/83-92 kostenfrei https://doaj.org/article/def66c345cf54be482673999440c8f7c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 106 2022 2
spelling	10.31489/2022m2/83-92 doi (DE-627)DOAJ09799359X (DE-599)DOAJdef66c345cf54be482673999440c8f7c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 B.I. Efendiev verfasserin aut An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found. fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality Analysis Analytic mechanics Probabilities. Mathematical statistics In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 106(2022), 2 (DE-627)DOAJ00015783X 26635011 nnns volume:106 year:2022 number:2 https://doi.org/10.31489/2022m2/83-92 kostenfrei https://doaj.org/article/def66c345cf54be482673999440c8f7c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 106 2022 2
allfields_unstemmed	10.31489/2022m2/83-92 doi (DE-627)DOAJ09799359X (DE-599)DOAJdef66c345cf54be482673999440c8f7c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 B.I. Efendiev verfasserin aut An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found. fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality Analysis Analytic mechanics Probabilities. Mathematical statistics In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 106(2022), 2 (DE-627)DOAJ00015783X 26635011 nnns volume:106 year:2022 number:2 https://doi.org/10.31489/2022m2/83-92 kostenfrei https://doaj.org/article/def66c345cf54be482673999440c8f7c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 106 2022 2
allfieldsGer	10.31489/2022m2/83-92 doi (DE-627)DOAJ09799359X (DE-599)DOAJdef66c345cf54be482673999440c8f7c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 B.I. Efendiev verfasserin aut An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found. fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality Analysis Analytic mechanics Probabilities. Mathematical statistics In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 106(2022), 2 (DE-627)DOAJ00015783X 26635011 nnns volume:106 year:2022 number:2 https://doi.org/10.31489/2022m2/83-92 kostenfrei https://doaj.org/article/def66c345cf54be482673999440c8f7c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 106 2022 2
allfieldsSound	10.31489/2022m2/83-92 doi (DE-627)DOAJ09799359X (DE-599)DOAJdef66c345cf54be482673999440c8f7c DE-627 ger DE-627 rakwb eng QA299.6-433 QA801-939 QA273-280 B.I. Efendiev verfasserin aut An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found. fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality Analysis Analytic mechanics Probabilities. Mathematical statistics In Қарағанды университетінің хабаршысы. Математика сериясы Academician Ye.A. Buketov Karaganda University, 2023 106(2022), 2 (DE-627)DOAJ00015783X 26635011 nnns volume:106 year:2022 number:2 https://doi.org/10.31489/2022m2/83-92 kostenfrei https://doaj.org/article/def66c345cf54be482673999440c8f7c kostenfrei http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 kostenfrei https://doaj.org/toc/2518-7929 Journal toc kostenfrei https://doaj.org/toc/2663-5011 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 106 2022 2
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topic_title	QA299.6-433 QA801-939 QA273-280 An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient fractional Riemann–Liouville integral fractional Riemann–Liouville derivative Gerasimov–Caputo fractional derivative Dirichlet problem Green’s function analogue of Lyapunov inequality
topic	misc QA299.6-433 misc QA801-939 misc QA273-280 misc fractional Riemann–Liouville integral misc fractional Riemann–Liouville derivative misc Gerasimov–Caputo fractional derivative misc Dirichlet problem misc Green’s function misc analogue of Lyapunov inequality misc Analysis misc Analytic mechanics misc Probabilities. Mathematical statistics
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title_sort	analogue of the lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient
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title_auth	An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient
abstract	This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found.
abstractGer	This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found.
abstract_unstemmed	This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found.
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title_short	An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient
url	https://doi.org/10.31489/2022m2/83-92 https://doaj.org/article/def66c345cf54be482673999440c8f7c http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/519 https://doaj.org/toc/2518-7929 https://doaj.org/toc/2663-5011
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doi_str	10.31489/2022m2/83-92
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up_date	2024-07-03T14:51:42.250Z
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An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient

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