Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator

Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](...
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Gespeichert in:

Autor*in:	Zhao, Yongshun [verfasserIn] Sun, Shurong Zhang, Yongxiang

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Boundary value problem Fractional difference equation -Laplacian operator Contraction mapping theorem Brouwer fixed point theorem

Anmerkung:	© Korean Society for Computational and Applied Mathematics 2016

Übergeordnetes Werk:	Enthalten in: Journal of applied mathematics and computing - Berlin : Springer, 2006, 54(2016), 1-2 vom: 31. März, Seite 183-197
Übergeordnetes Werk:	volume:54 ; year:2016 ; number:1-2 ; day:31 ; month:03 ; pages:183-197

Links:	Volltext

DOI / URN:	10.1007/s12190-016-1003-1

Katalog-ID:	SPR025156713

Internformat


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245	1	0	\|a Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
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520			\|a Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem.
650		4	\|a Boundary value problem \|7 (dpeaa)DE-He213
650		4	\|a Fractional difference equation \|7 (dpeaa)DE-He213
650		4	\|a -Laplacian operator \|7 (dpeaa)DE-He213
650		4	\|a Contraction mapping theorem \|7 (dpeaa)DE-He213
650		4	\|a Brouwer fixed point theorem \|7 (dpeaa)DE-He213
700	1		\|a Sun, Shurong \|4 aut
700	1		\|a Zhang, Yongxiang \|4 aut
773	0	8	\|i Enthalten in \|t Journal of applied mathematics and computing \|d Berlin : Springer, 2006 \|g 54(2016), 1-2 vom: 31. März, Seite 183-197 \|w (DE-627)565516833 \|w (DE-600)2424171-4 \|x 1865-2085 \|7 nnns
773	1	8	\|g volume:54 \|g year:2016 \|g number:1-2 \|g day:31 \|g month:03 \|g pages:183-197
856	4	0	\|u https://dx.doi.org/10.1007/s12190-016-1003-1 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_165
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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matchkey_str	article:18652085:2016----::xsecadnqeesfouintarcinlifrneqai
hierarchy_sort_str	2016
publishDate	2016
allfields	10.1007/s12190-016-1003-1 doi (DE-627)SPR025156713 (SPR)s12190-016-1003-1-e DE-627 ger DE-627 rakwb eng Zhao, Yongshun verfasserin aut Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Korean Society for Computational and Applied Mathematics 2016 Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213 Sun, Shurong aut Zhang, Yongxiang aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 54(2016), 1-2 vom: 31. März, Seite 183-197 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197 https://dx.doi.org/10.1007/s12190-016-1003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 54 2016 1-2 31 03 183-197
spelling	10.1007/s12190-016-1003-1 doi (DE-627)SPR025156713 (SPR)s12190-016-1003-1-e DE-627 ger DE-627 rakwb eng Zhao, Yongshun verfasserin aut Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Korean Society for Computational and Applied Mathematics 2016 Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213 Sun, Shurong aut Zhang, Yongxiang aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 54(2016), 1-2 vom: 31. März, Seite 183-197 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197 https://dx.doi.org/10.1007/s12190-016-1003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 54 2016 1-2 31 03 183-197
allfields_unstemmed	10.1007/s12190-016-1003-1 doi (DE-627)SPR025156713 (SPR)s12190-016-1003-1-e DE-627 ger DE-627 rakwb eng Zhao, Yongshun verfasserin aut Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Korean Society for Computational and Applied Mathematics 2016 Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213 Sun, Shurong aut Zhang, Yongxiang aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 54(2016), 1-2 vom: 31. März, Seite 183-197 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197 https://dx.doi.org/10.1007/s12190-016-1003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 54 2016 1-2 31 03 183-197
allfieldsGer	10.1007/s12190-016-1003-1 doi (DE-627)SPR025156713 (SPR)s12190-016-1003-1-e DE-627 ger DE-627 rakwb eng Zhao, Yongshun verfasserin aut Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Korean Society for Computational and Applied Mathematics 2016 Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213 Sun, Shurong aut Zhang, Yongxiang aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 54(2016), 1-2 vom: 31. März, Seite 183-197 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197 https://dx.doi.org/10.1007/s12190-016-1003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 54 2016 1-2 31 03 183-197
allfieldsSound	10.1007/s12190-016-1003-1 doi (DE-627)SPR025156713 (SPR)s12190-016-1003-1-e DE-627 ger DE-627 rakwb eng Zhao, Yongshun verfasserin aut Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Korean Society for Computational and Applied Mathematics 2016 Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213 Sun, Shurong aut Zhang, Yongxiang aut Enthalten in Journal of applied mathematics and computing Berlin : Springer, 2006 54(2016), 1-2 vom: 31. März, Seite 183-197 (DE-627)565516833 (DE-600)2424171-4 1865-2085 nnns volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197 https://dx.doi.org/10.1007/s12190-016-1003-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 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_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 54 2016 1-2 31 03 183-197
language	English
source	Enthalten in Journal of applied mathematics and computing 54(2016), 1-2 vom: 31. März, Seite 183-197 volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197
sourceStr	Enthalten in Journal of applied mathematics and computing 54(2016), 1-2 vom: 31. März, Seite 183-197 volume:54 year:2016 number:1-2 day:31 month:03 pages:183-197
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Boundary value problem Fractional difference equation -Laplacian operator Contraction mapping theorem Brouwer fixed point theorem
isfreeaccess_bool	false
container_title	Journal of applied mathematics and computing
authorswithroles_txt_mv	Zhao, Yongshun @@aut@@ Sun, Shurong @@aut@@ Zhang, Yongxiang @@aut@@
publishDateDaySort_date	2016-03-31T00:00:00Z
hierarchy_top_id	565516833
id	SPR025156713
language_de	englisch
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author	Zhao, Yongshun
spellingShingle	Zhao, Yongshun misc Boundary value problem misc Fractional difference equation misc -Laplacian operator misc Contraction mapping theorem misc Brouwer fixed point theorem Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
authorStr	Zhao, Yongshun
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topic_title	Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator Boundary value problem (dpeaa)DE-He213 Fractional difference equation (dpeaa)DE-He213 -Laplacian operator (dpeaa)DE-He213 Contraction mapping theorem (dpeaa)DE-He213 Brouwer fixed point theorem (dpeaa)DE-He213
topic	misc Boundary value problem misc Fractional difference equation misc -Laplacian operator misc Contraction mapping theorem misc Brouwer fixed point theorem
topic_unstemmed	misc Boundary value problem misc Fractional difference equation misc -Laplacian operator misc Contraction mapping theorem misc Brouwer fixed point theorem
topic_browse	misc Boundary value problem misc Fractional difference equation misc -Laplacian operator misc Contraction mapping theorem misc Brouwer fixed point theorem
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
ctrlnum	(DE-627)SPR025156713 (SPR)s12190-016-1003-1-e
title_full	Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
author_sort	Zhao, Yongshun
journal	Journal of applied mathematics and computing
journalStr	Journal of applied mathematics and computing
lang_code	eng
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publishDateSort	2016
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container_start_page	183
author_browse	Zhao, Yongshun Sun, Shurong Zhang, Yongxiang
container_volume	54
format_se	Elektronische Aufsätze
author-letter	Zhao, Yongshun
doi_str_mv	10.1007/s12190-016-1003-1
title_sort	existence and uniqueness of solutions to a fractional difference equation with p-laplacian operator
title_auth	Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
abstract	Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. © Korean Society for Computational and Applied Mathematics 2016
abstractGer	Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. © Korean Society for Computational and Applied Mathematics 2016
abstract_unstemmed	Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem. © Korean Society for Computational and Applied Mathematics 2016
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title_short	Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator
url	https://dx.doi.org/10.1007/s12190-016-1003-1
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author2	Sun, Shurong Zhang, Yongxiang
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doi_str	10.1007/s12190-016-1003-1
up_date	2024-07-03T14:12:55.495Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025156713</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403063758.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2016 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12190-016-1003-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025156713</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12190-016-1003-1-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zhao, Yongshun</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Korean Society for Computational and Applied Mathematics 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form Δβ[ϕp(Δαy)](t)+f(α+β+t-1,y(α+β+t-1))=0,t∈[0,b]N0,Δαy(β-2)=Δαy(β+b)=0,y(α+β-4)=y(α+β+b)=0,%$\begin{aligned} {\left\{ \begin{array}{ll}\Delta ^{\beta }[\phi _{p}(\Delta ^{\alpha }y)](t)+f(\alpha +\beta +t-1,y(\alpha +\beta +t-1))=0, t\in [0,b]_{{\mathbb {N}}_{0}},\\ \Delta ^{\alpha }y(\beta -2)=\Delta ^{\alpha }y(\beta +b)=0,\\ y(\alpha +\beta -4)=y(\alpha +\beta +b)=0,\end{array}\right. } \end{aligned}%$where %$f:[\alpha +\beta -4,\alpha +\beta +b]_{{\mathbb {N}}_{\alpha +\beta -4}}\times {\mathbb {R}}\rightarrow {\mathbb {R}}%$ is a continuous function, and %$p>1%$, %$1<\alpha ,\beta \le 2%$. 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Existence and uniqueness of solutions to a fractional difference equation with p-Laplacian operator

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