New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications

Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new conc...
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Autor*in:	Wang, Yizhu [verfasserIn] Liu, Yiding [verfasserIn] Hou, Chengmin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Quantum calculus -derivative Boundary value problem Initial value problem

Übergeordnetes Werk:	Enthalten in: Advances in difference equations - [S.l.] : Springer International, 2004, 2018(2018), 1 vom: 28. Aug.
Übergeordnetes Werk:	volume:2018 ; year:2018 ; number:1 ; day:28 ; month:08

Links:	Volltext

DOI / URN:	10.1186/s13662-018-1753-1

Katalog-ID:	SPR032109210

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allfields	10.1186/s13662-018-1753-1 doi (DE-627)SPR032109210 (SPR)s13662-018-1753-1-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Wang, Yizhu verfasserin aut New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations. Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213 Liu, Yiding verfasserin aut Hou, Chengmin verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2018(2018), 1 vom: 28. Aug. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2018 year:2018 number:1 day:28 month:08 https://dx.doi.org/10.1186/s13662-018-1753-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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 31.49 ASE AR 2018 2018 1 28 08
spelling	10.1186/s13662-018-1753-1 doi (DE-627)SPR032109210 (SPR)s13662-018-1753-1-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Wang, Yizhu verfasserin aut New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations. Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213 Liu, Yiding verfasserin aut Hou, Chengmin verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2018(2018), 1 vom: 28. Aug. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2018 year:2018 number:1 day:28 month:08 https://dx.doi.org/10.1186/s13662-018-1753-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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 31.49 ASE AR 2018 2018 1 28 08
allfields_unstemmed	10.1186/s13662-018-1753-1 doi (DE-627)SPR032109210 (SPR)s13662-018-1753-1-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Wang, Yizhu verfasserin aut New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations. Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213 Liu, Yiding verfasserin aut Hou, Chengmin verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2018(2018), 1 vom: 28. Aug. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2018 year:2018 number:1 day:28 month:08 https://dx.doi.org/10.1186/s13662-018-1753-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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 31.49 ASE AR 2018 2018 1 28 08
allfieldsGer	10.1186/s13662-018-1753-1 doi (DE-627)SPR032109210 (SPR)s13662-018-1753-1-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Wang, Yizhu verfasserin aut New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations. Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213 Liu, Yiding verfasserin aut Hou, Chengmin verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2018(2018), 1 vom: 28. Aug. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2018 year:2018 number:1 day:28 month:08 https://dx.doi.org/10.1186/s13662-018-1753-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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 31.49 ASE AR 2018 2018 1 28 08
allfieldsSound	10.1186/s13662-018-1753-1 doi (DE-627)SPR032109210 (SPR)s13662-018-1753-1-e DE-627 ger DE-627 rakwb eng 510 610 ASE 31.49 bkl Wang, Yizhu verfasserin aut New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations. Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213 Liu, Yiding verfasserin aut Hou, Chengmin verfasserin aut Enthalten in Advances in difference equations [S.l.] : Springer International, 2004 2018(2018), 1 vom: 28. Aug. (DE-627)377755699 (DE-600)2132815-8 1687-1847 nnns volume:2018 year:2018 number:1 day:28 month:08 https://dx.doi.org/10.1186/s13662-018-1753-1 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE 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 31.49 ASE AR 2018 2018 1 28 08
language	English
source	Enthalten in Advances in difference equations 2018(2018), 1 vom: 28. Aug. volume:2018 year:2018 number:1 day:28 month:08
sourceStr	Enthalten in Advances in difference equations 2018(2018), 1 vom: 28. Aug. volume:2018 year:2018 number:1 day:28 month:08
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Quantum calculus -derivative Boundary value problem Initial value problem
dewey-raw	510
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container_title	Advances in difference equations
authorswithroles_txt_mv	Wang, Yizhu @@aut@@ Liu, Yiding @@aut@@ Hou, Chengmin @@aut@@
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New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. 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author	Wang, Yizhu
spellingShingle	Wang, Yizhu ddc 510 bkl 31.49 misc Quantum calculus misc -derivative misc Boundary value problem misc Initial value problem New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications
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topic_title	510 610 ASE 31.49 bkl New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications Quantum calculus (dpeaa)DE-He213 -derivative (dpeaa)DE-He213 Boundary value problem (dpeaa)DE-He213 Initial value problem (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc Quantum calculus misc -derivative misc Boundary value problem misc Initial value problem
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title	New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications
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title_full	New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications
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title_sort	new concepts of fractional hahn’s $q,\omega $-derivative of riemann–liouville type and caputo type and applications
title_auth	New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications
abstract	Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations.
abstractGer	Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations.
abstract_unstemmed	Abstract In this paper, we give the definitions of $q,\omega $-exponential function and $q,\omega $-gamma function. New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type are introduced, meanwhile we discuss some properties. As applications of the new concepts, we give the existence result of positive solutions for boundary value problem of fractional $q,\omega $-derivatives equations. We also definite certain $q,\omega $-Mittag-Leffler function by solving the initial value problem of fractional $q,\omega $-equations.
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title_short	New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications
url	https://dx.doi.org/10.1186/s13662-018-1753-1
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score	7.402011

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New concepts of fractional Hahn’s $q,\omega $-derivative of Riemann–Liouville type and Caputo type and applications

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