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An Application of Nabla Operator for the Radial Schrödinger Equation

Year 2017, Volume: 7 Issue: 3, 199 - 208, 30.09.2017

Abstract

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



References

  • 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

Year 2017, Volume: 7 Issue: 3, 199 - 208, 30.09.2017

Abstract

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



References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Matematik / Mathematics
Authors

Reşat Yılmazer

Publication Date September 30, 2017
Submission Date January 19, 2017
Acceptance Date June 3, 2017
Published in Issue Year 2017 Volume: 7 Issue: 3

Cite

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.
AMA Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. J. Inst. Sci. and Tech. September 2017;7(3):199-208.
Chicago Yılmazer, Reşat. “An Application of Nabla Operator for the Radial Schrödinger Equation”. Journal of the Institute of Science and Technology 7, no. 3 (September 2017): 199-208.
EndNote Yılmazer R (September 1, 2017) An Application of Nabla Operator for the Radial Schrödinger Equation. Journal of the Institute of Science and Technology 7 3 199–208.
IEEE R. Yılmazer, “An Application of Nabla Operator for the Radial Schrödinger Equation”, J. Inst. Sci. and Tech., vol. 7, no. 3, pp. 199–208, 2017.
ISNAD Yılmazer, Reşat. “An Application of Nabla Operator for the Radial Schrödinger Equation”. Journal of the Institute of Science and Technology 7/3 (September 2017), 199-208.
JAMA Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. J. Inst. Sci. and Tech. 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, vol. 7, no. 3, 2017, pp. 199-08.
Vancouver Yılmazer R. An Application of Nabla Operator for the Radial Schrödinger Equation. J. Inst. Sci. and Tech. 2017;7(3):199-208.