An Application of Nabla Operator for the Radial Schrödinger Equation

Yıl 2017, Cilt: 7 Sayı: 3, 199 - 208, 30.09.2017

Reşat Yılmazer

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

Anahtar Kelimeler

Fractional calculus, discrete fractional calculus, nabla operator, radial Schrödinger equation

Radyal Schrödinger Denklemi İçin Nabla Operatörünün Bir Uygulaması

Öz

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

Anahtar Kelimeler

Kesirli hesap, ayrık kesirli hesap, nabla operatörü, radyal Schrödinger denklemi

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.