On nonlocal fractional sum-difference boundary value problems for Caputo fractional functional difference equations with delay
In this article, we study the existence and uniqueness results for a nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction principle. Finally, we present some e...
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| Vydáno v: | Advances in difference equations Ročník 2017; číslo 1; s. 1 - 14 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Springer International Publishing
01.08.2017
Springer Nature B.V SpringerOpen |
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| ISSN: | 1687-1847, 1687-1839, 1687-1847 |
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| Abstract | In this article, we study the existence and uniqueness results for a nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction principle. Finally, we present some examples to display the importance of these results. |
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| AbstractList | In this article, we study the existence and uniqueness results for a nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction principle. Finally, we present some examples to display the importance of these results. Abstract In this article, we study the existence and uniqueness results for a nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction principle. Finally, we present some examples to display the importance of these results. |
| ArticleNumber | 219 |
| Author | Sitthiwirattham, Thanin Kaewwisetkul, Bunjong |
| Author_xml | – sequence: 1 givenname: Bunjong surname: Kaewwisetkul fullname: Kaewwisetkul, Bunjong organization: Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin – sequence: 2 givenname: Thanin orcidid: 0000-0002-8455-1402 surname: Sitthiwirattham fullname: Sitthiwirattham, Thanin email: thanin.s@sci.kmutnb.ac.th organization: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Mathematics Department, Faculty of Science and Technology, Suan Dusit University |
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Appl.201625409414361577606712505 – reference: WuGCBaleanuDDiscrete fractional logistic map and its chaosNonlinear Dyn.201475283287314485210.1007/s11071-013-1065-71281.34121 – reference: SitthiwiratthamTTariboonJNtouyasSKExistence results for fractional difference equations with three-point fractional sum boundary conditionsDiscrete Dyn. Nat. Soc.20132013309722310.1155/2013/104276 – reference: LaoprasittichokSSitthiwiratthamTOn a fractional difference-sum boundary value problems for fractional difference equations involving sequential fractional differences via different ordersJ. Comput. Anal. Appl.201723610971111 – reference: AbdeljawadTOn Riemann and Caputo fractional differencesComput. Math. Appl.201162316021611282474710.1016/j.camwa.2011.03.0361228.26008 – reference: AticiFMEloePWA transform method in discrete fractional calculusInt. J. Differ. Equ.2007221651762493595 – reference: SitthiwiratthamTExistence and uniqueness of solutions of sequential nonlinear fractional difference equations with three-point fractional sum boundary conditionsMath. Methods Appl. Sci.20153828092815338270710.1002/mma.32631334.39023 – reference: GoodrichCSPetersonACDiscrete Fractional Calculus2015New YorkSpringer10.1007/978-3-319-25562-01350.39001 – reference: SitthiwiratthamTBoundary value problem for p-Laplacian Caputo fractional difference equations with fractional sum boundary conditionsMath. Methods Appl. Sci.201639615221534348351310.1002/mma.35861336.39001 – reference: GoodrichCSOn a discrete fractional three-point boundary value problemJ. Differ. Equ. Appl.201218397415290182910.1080/10236198.2010.5032401253.26010 – reference: ReunsumritJSitthiwiratthamTPositive solutions of three-point fractional sum boundary value problem for Caputo fractional difference equations via an argument with a shiftPositivity2016204861876356817410.1007/s11117-015-0391-z1362.39012 – reference: GoodrichCSOn semipositone discrete fractional boundary value problems with non-local boundary conditionsJ. Differ. Equ. Appl.20131917581780317351610.1080/10236198.2013.7752591282.26008 – reference: FerreiraRExistence and uniqueness of solution to some discrete fractional boundary value problems of order less than oneJ. Differ. Equ. Appl.201319712718304905010.1080/10236198.2012.6825771276.26013 – reference: SitthiwiratthamTTariboonJNtouyasSKBoundary value problems for fractional difference equations with three-point fractional sum boundary conditionsAdv. Differ. Equ.20132013321306710.1186/1687-1847-2013-296 – reference: ReunsumritJSitthiwiratthamTOn positive solutions to fractional sum boundary value problems for nonlinear fractional difference equationsMath. Methods Appl. Sci.2016391027372751351277910.1002/mma.37251342.39001 – reference: AgarwalRPBaleanuDRezapourSSalehiSThe existence of solutions for some fractional finite difference equations via sum boundary conditionsAdv. Differ. Equ.20142014337474010.1186/1687-1847-2014-282 – reference: AticiFMEloePWTwo-point boundary value problems for finite fractional difference equationsJ. Differ. Equ. Appl.201117445456278335910.1080/102361909030292411215.39002 – volume: 38 start-page: 2809 year: 2015 ident: 1283_CR15 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3263 – volume: 25 start-page: 409 year: 2016 ident: 1283_CR20 publication-title: Dyn. Syst. Appl. – volume: 23 start-page: 1097 issue: 6 year: 2017 ident: 1283_CR21 publication-title: J. Comput. Anal. 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| SubjectTerms | Analysis boundary value problem Boundary value problems Caputo fractional functional difference equations Delay Difference and Functional Equations Difference equations existence Functional Analysis Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Schauder fixpoint theorem Uniqueness |
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| Title | On nonlocal fractional sum-difference boundary value problems for Caputo fractional functional difference equations with delay |
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