Araştırma Makalesi
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An Application of Nabla Operator for the Radial Schrödinger Equation

Yıl 2017, Cilt: 7 Sayı: 3, 199 - 208, 30.09.2017
https://izlik.org/JA47MG53TE

Öz

The aim of this present study is to obtain the discrete fractional solutions of the radial Schrödinger
equation by applying the nabla discrete fractional calculus (DFC) operator



Kaynakça

  • Abdeljawad T, Atici FM, 2012. On the definitions of nabla fractional operators. Abstr. Appl. Anal., 2012: 13p.
  • Atici FM, Acar N, 2013. Exponential functions of discrete fractional calculus. Appl. Anal. Discrete Math., 7: 343-353.
  • Atici FM, Eloe PW, 2009. Discrete fractional calculus with the nabla operator. Electron. J. Qual. Theory Differ. Equ., 3: 1-12.
  • Diaz JB, Osler TJ, 1974. Differences of fractional order. Amer. Math. Soc., 28: 185-202.
  • Gray HL, Zhang N, 1988. On a new definition of the fractional difference. Math. Comp., 50: 513-529.
  • Inc M, Yilmazer R, 2016. On some particular solutions of the Chebyshev’s equation by means of ∇^α discrete fractional calculus operator. Progr. Fract. Differ. Appl., 2 (2): 123-129.
  • Jarad F, Kaymacalan B, Tas K, 2012. A new transform method in nabla discrete fractional calculus. Adv. Difference Equ., 190, doi: 10.1186/1687-1847-2012-190.
  • Jonnalagadda JM, 2015. Analysis of nonlinear fractional nabla difference equations. Int. J. Anal. Appl., 7 (1): 79-95.
  • Kuttner B, 1957. On differences of fractional order. Proc. London Math. Soc., 3: 453-466.
  • Miller KS, Ross B, 1989. Fractional difference calculus. Ellis Horwood Ser. Math. Appl., 139-152.
  • Ozturk O, 2016. A study on nabla discrete fractional operator in mass-spring-damper system. New Trends Math. Sci., 4 (4): 137-144.
  • Ozturk O, Yilmazer R, 2016. Solutions of the radial component of the fractional Schrödinger equation using N-fractional calculus operator. Differ. Equ. Dyn. Syst., doi: 10.1007/s12591-016-0308-8.
  • Yilmazer R, Inc M, Tchier F, Baleanu D, 2016. Particular solutions of the confluent hypergeometric differential equation by using the nabla fractional calculus operator. Entropy, 18 (2): 49.
  • Yilmazer R, Ozturk O, 2012. N-fractional calculus operator N^η method applied to a Gegenbauer differential equation. Cankaya Univ. J. Sci. Eng., 9 (1): 37-48.
  • Yilmazer R, Ozturk O, 2013. Explicit solutions of singular differential equation by means of fractional calculus operators. Abstr. Appl. Anal., 2013: 6p.

Radyal Schrödinger Denklemi İçin Nabla Operatörünün Bir Uygulaması

Yıl 2017, Cilt: 7 Sayı: 3, 199 - 208, 30.09.2017
https://izlik.org/JA47MG53TE

Öz

Bu çalışmanın amacı, nabla ayrık kesirli hesap operatörünün uygulanmasıyla radyal Schrödinger
denkleminin ayrık kesirli çözümlerini elde etmektir.



Kaynakça

  • Abdeljawad T, Atici FM, 2012. On the definitions of nabla fractional operators. Abstr. Appl. Anal., 2012: 13p.
  • Atici FM, Acar N, 2013. Exponential functions of discrete fractional calculus. Appl. Anal. Discrete Math., 7: 343-353.
  • Atici FM, Eloe PW, 2009. Discrete fractional calculus with the nabla operator. Electron. J. Qual. Theory Differ. Equ., 3: 1-12.
  • Diaz JB, Osler TJ, 1974. Differences of fractional order. Amer. Math. Soc., 28: 185-202.
  • Gray HL, Zhang N, 1988. On a new definition of the fractional difference. Math. Comp., 50: 513-529.
  • Inc M, Yilmazer R, 2016. On some particular solutions of the Chebyshev’s equation by means of ∇^α discrete fractional calculus operator. Progr. Fract. Differ. Appl., 2 (2): 123-129.
  • Jarad F, Kaymacalan B, Tas K, 2012. A new transform method in nabla discrete fractional calculus. Adv. Difference Equ., 190, doi: 10.1186/1687-1847-2012-190.
  • Jonnalagadda JM, 2015. Analysis of nonlinear fractional nabla difference equations. Int. J. Anal. Appl., 7 (1): 79-95.
  • Kuttner B, 1957. On differences of fractional order. Proc. London Math. Soc., 3: 453-466.
  • Miller KS, Ross B, 1989. Fractional difference calculus. Ellis Horwood Ser. Math. Appl., 139-152.
  • Ozturk O, 2016. A study on nabla discrete fractional operator in mass-spring-damper system. New Trends Math. Sci., 4 (4): 137-144.
  • Ozturk O, Yilmazer R, 2016. Solutions of the radial component of the fractional Schrödinger equation using N-fractional calculus operator. Differ. Equ. Dyn. Syst., doi: 10.1007/s12591-016-0308-8.
  • Yilmazer R, Inc M, Tchier F, Baleanu D, 2016. Particular solutions of the confluent hypergeometric differential equation by using the nabla fractional calculus operator. Entropy, 18 (2): 49.
  • Yilmazer R, Ozturk O, 2012. N-fractional calculus operator N^η method applied to a Gegenbauer differential equation. Cankaya Univ. J. Sci. Eng., 9 (1): 37-48.
  • Yilmazer R, Ozturk O, 2013. Explicit solutions of singular differential equation by means of fractional calculus operators. Abstr. Appl. Anal., 2013: 6p.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Reşat Yılmazer

Gönderilme Tarihi 19 Ocak 2017
Kabul Tarihi 3 Haziran 2017
Yayımlanma Tarihi 30 Eylül 2017
IZ https://izlik.org/JA47MG53TE
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 3

Kaynak Göster

APA Yılmazer, R. (2017). An Application of Nabla Operator for the Radial Schrödinger Equation. Journal of the Institute of Science and Technology, 7(3), 199-208. https://izlik.org/JA47MG53TE
AMA 1.Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. Iğdır Üniv. Fen Bil Enst. Der. 2017;7(3):199-208. https://izlik.org/JA47MG53TE
Chicago Yılmazer, Reşat. 2017. “An Application of Nabla Operator for the Radial Schrödinger Equation”. Journal of the Institute of Science and Technology 7 (3): 199-208. https://izlik.org/JA47MG53TE.
EndNote Yılmazer R (01 Eylül 2017) An Application of Nabla Operator for the Radial Schrödinger Equation. Journal of the Institute of Science and Technology 7 3 199–208.
IEEE [1]R. Yılmazer, “An Application of Nabla Operator for the Radial Schrödinger Equation”, Iğdır Üniv. Fen Bil Enst. Der., c. 7, sy 3, ss. 199–208, Eyl. 2017, [çevrimiçi]. Erişim adresi: https://izlik.org/JA47MG53TE
ISNAD Yılmazer, Reşat. “An Application of Nabla Operator for the Radial Schrödinger Equation”. Journal of the Institute of Science and Technology 7/3 (01 Eylül 2017): 199-208. https://izlik.org/JA47MG53TE.
JAMA 1.Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. Iğdır Üniv. Fen Bil Enst. Der. 2017;7:199–208.
MLA Yılmazer, Reşat. “An Application of Nabla Operator for the Radial Schrödinger Equation”. Journal of the Institute of Science and Technology, c. 7, sy 3, Eylül 2017, ss. 199-08, https://izlik.org/JA47MG53TE.
Vancouver 1.Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. Iğdır Üniv. Fen Bil Enst. Der. [Internet]. 01 Eylül 2017;7(3):199-208. Erişim adresi: https://izlik.org/JA47MG53TE