Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative

By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Bin Zheng [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Übergeordnetes Werk:	In: Journal of Applied Mathematics - Hindawi Limited, 2006, (2013)
Übergeordnetes Werk:	year:2013

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

DOI / URN:	10.1155/2013/341706

Katalog-ID:	DOAJ037184113

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allfieldsSound	10.1155/2013/341706 doi (DE-627)DOAJ037184113 (DE-599)DOAJ4867596083134156b4d44b8720dd7895 DE-627 ger DE-627 rakwb eng QA1-939 Bin Zheng verfasserin aut Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the literature. Then, we apply the results established to research the boundedness, uniqueness, and continuous dependence on the initial value for the solution to a certain fractional differential equation. Mathematics In Journal of Applied Mathematics Hindawi Limited, 2006 (2013) (DE-627)638066859 (DE-600)2578385-3 16870042 nnns year:2013 https://doi.org/10.1155/2013/341706 kostenfrei https://doaj.org/article/4867596083134156b4d44b8720dd7895 kostenfrei http://dx.doi.org/10.1155/2013/341706 kostenfrei https://doaj.org/toc/1110-757X Journal toc kostenfrei https://doaj.org/toc/1687-0042 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 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_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2088 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 2013
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topic_title	QA1-939 Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
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title	Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
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title_full	Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
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title_sort	some new gronwall-bellman-type inequalities based on the modified riemann-liouville fractional derivative
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title_auth	Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
abstract	By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the literature. Then, we apply the results established to research the boundedness, uniqueness, and continuous dependence on the initial value for the solution to a certain fractional differential equation.
abstractGer	By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the literature. Then, we apply the results established to research the boundedness, uniqueness, and continuous dependence on the initial value for the solution to a certain fractional differential equation.
abstract_unstemmed	By use of the properties of the modified Riemann-Liouville fractional derivative, some new Gronwall-Bellman-type inequalities are researched. First, we derive some new explicit bounds for the unknown functions lying in these inequalities, which are of different forms from some existing bounds in the literature. Then, we apply the results established to research the boundedness, uniqueness, and continuous dependence on the initial value for the solution to a certain fractional differential equation.
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title_short	Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative
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up_date	2024-07-04T00:15:03.641Z
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Some New Gronwall-Bellman-Type Inequalities Based on the Modified Riemann-Liouville Fractional Derivative

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