Theory of nth-order linear general quantum difference equations

Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Nashat Faried [verfasserIn] Enas M. Shehata [verfasserIn] Rasha M. El Zafarani [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations

Übergeordnetes Werk:	In: Advances in Difference Equations - SpringerOpen, 2006, (2018), 1, Seite 24
Übergeordnetes Werk:	year:2018 ; number:1 ; pages:24

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1186/s13662-018-1715-7

Katalog-ID:	DOAJ07370251X

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allfields	10.1186/s13662-018-1715-7 doi (DE-627)DOAJ07370251X (DE-599)DOAJ39c9583a49ee44c0a233d72823087eec DE-627 ger DE-627 rakwb eng QA1-939 Nashat Faried verfasserin aut Theory of nth-order linear general quantum difference equations 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations. A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations Mathematics Enas M. Shehata verfasserin aut Rasha M. El Zafarani verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2018), 1, Seite 24 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2018 number:1 pages:24 https://doi.org/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/article/39c9583a49ee44c0a233d72823087eec kostenfrei http://link.springer.com/article/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 24
spelling	10.1186/s13662-018-1715-7 doi (DE-627)DOAJ07370251X (DE-599)DOAJ39c9583a49ee44c0a233d72823087eec DE-627 ger DE-627 rakwb eng QA1-939 Nashat Faried verfasserin aut Theory of nth-order linear general quantum difference equations 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations. A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations Mathematics Enas M. Shehata verfasserin aut Rasha M. El Zafarani verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2018), 1, Seite 24 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2018 number:1 pages:24 https://doi.org/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/article/39c9583a49ee44c0a233d72823087eec kostenfrei http://link.springer.com/article/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 24
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allfieldsSound	10.1186/s13662-018-1715-7 doi (DE-627)DOAJ07370251X (DE-599)DOAJ39c9583a49ee44c0a233d72823087eec DE-627 ger DE-627 rakwb eng QA1-939 Nashat Faried verfasserin aut Theory of nth-order linear general quantum difference equations 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations. A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations Mathematics Enas M. Shehata verfasserin aut Rasha M. El Zafarani verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2018), 1, Seite 24 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2018 number:1 pages:24 https://doi.org/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/article/39c9583a49ee44c0a233d72823087eec kostenfrei http://link.springer.com/article/10.1186/s13662-018-1715-7 kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 24
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topic_facet	A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations Mathematics
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callnumber-first	Q - Science
author	Nashat Faried
spellingShingle	Nashat Faried misc QA1-939 misc A general quantum difference operator misc nth-order linear general quantum difference equations misc β-Wronskian misc Homogeneous quantum difference equations misc Non-homogeneous quantum difference equations misc Mathematics Theory of nth-order linear general quantum difference equations
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topic_title	QA1-939 Theory of nth-order linear general quantum difference equations A general quantum difference operator nth-order linear general quantum difference equations β-Wronskian Homogeneous quantum difference equations Non-homogeneous quantum difference equations
topic	misc QA1-939 misc A general quantum difference operator misc nth-order linear general quantum difference equations misc β-Wronskian misc Homogeneous quantum difference equations misc Non-homogeneous quantum difference equations misc Mathematics
topic_unstemmed	misc QA1-939 misc A general quantum difference operator misc nth-order linear general quantum difference equations misc β-Wronskian misc Homogeneous quantum difference equations misc Non-homogeneous quantum difference equations misc Mathematics
topic_browse	misc QA1-939 misc A general quantum difference operator misc nth-order linear general quantum difference equations misc β-Wronskian misc Homogeneous quantum difference equations misc Non-homogeneous quantum difference equations misc Mathematics
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title	Theory of nth-order linear general quantum difference equations
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title_full	Theory of nth-order linear general quantum difference equations
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title_sort	theory of nth-order linear general quantum difference equations
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title_auth	Theory of nth-order linear general quantum difference equations
abstract	Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations.
abstractGer	Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations.
abstract_unstemmed	Abstract In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator Dβ $D_{\beta }$ which is defined by Dβf(t)=(f(β(t))−f(t))/(β(t)−t) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$, β(t)≠t $\beta (t)\neq t$, where β is a strictly increasing continuous function defined on an interval I⊆R $I\subseteq \mathbb{R}$ that has only one fixed point s0∈I $s_{0}\in {I}$. We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with Dβ $D_{\beta }$, and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations.
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title_short	Theory of nth-order linear general quantum difference equations
url	https://doi.org/10.1186/s13662-018-1715-7 https://doaj.org/article/39c9583a49ee44c0a233d72823087eec http://link.springer.com/article/10.1186/s13662-018-1715-7 https://doaj.org/toc/1687-1847
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up_date	2024-07-03T19:09:33.820Z
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Theory of nth-order linear general quantum difference equations

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