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ON DISCRETE FRACTIONAL SOLUTIONS OF THE HYDROGEN ATOM TYPE EQUATIONS

ABSTRACT
Discrete fractional calculus deals with sums and differences of arbitrary orders. In this study, we acquire new discrete fractional solutions (dfs) of hydrogen atom type equations (HAEs) by using discrete fractional nabla operator α(0 < α < 1). This operator is applied homogeneous and nonhomogeneous HAEs. So, we obtain many particular solutions of these equations.
KEYWORDS
PAPER SUBMITTED: 2019-03-11
PAPER REVISED: 2019-07-10
PAPER ACCEPTED: 2019-08-02
PUBLISHED ONLINE: 2019-09-15
DOI REFERENCE: https://doi.org/10.2298/TSCI190311354Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S1935 - S1941]
REFERENCES
  1. Podlubny, I., Fractional Differential Equations, Academic Press, New York, 1999
  2. Oldham, K., Spanier, J., The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Dover Publications, Inc., Mineola, New York, 2002
  3. Sabatier, J., et al., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007
  4. Kuttner, B., On Differences of Fractional Order, Proceeding of the London Mathematical Society 3 (1957), 453-466
  5. Diaz J.B., Osler, T.J., Differences of Fractional Order, American Mathematical Society, 28 (1974), 185-202
  6. Atıcı, F.M., Eloe, P.W., Discrete Fractional Calculus with the Nabla Operator, Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed I, 3 (2009), 1-12
  7. Atıcı, F.M., Eloe, P.W., Gronwall's Inequality on Discrete Fractional Calculus, Comput. Math. Appl., 64 (2012), 3193-3200
  8. Acar, N., Atıcı, F.M., Exponential Functions of Discrete Fractional Calculus, Appl. Anal. Discrete Math. 7 (2013), 343-353
  9. Dehghan, M., et al., The Solution of the Linear Fractional Partial Differential Equations Using the Homotopy Analysis Method, Z Naturforsch 65a (2010) 935-949.
  10. Manafian, J., Bolghar, P., Numerical Solutions of Nonlinear 3-Dimensional Volterra Integral-Differential Equations with 3D-Block-Pulse Functions, Mathematical Methods in the Applied Sciences, 41(12) (2018), 4867-4876
  11. Mohan, J.J., Solutions of Perturbed Nonlinear Nabla Fractional Difference Equations, Novi Sad. J. Math. 43 (2013), 125-138
  12. Mohan, J.J., Analysis of Nonlinear Fractional Nabla Difference Equations, Int. J. Analysis Applications 7 (2015), 79-95
  13. Granger, C. W. J., Joyeux, R., An Introduction to Long-Memory Time Series Models and Fractional Differencing, J. Time Ser. Anal., 1 (1980), 15-29
  14. Hosking, J. R. M., Fractional Differencing, Biometrika, 68 (1981), 165-176
  15. Gray, H.L., Zhang, N., On a New Definition of the Fractional Difference, Mathematics of Computation, 50 (182) (1988), 513-529
  16. Levitan, B.M., Sargsyan, I.S., Introduction to Spectral Theory, Moscow, Nauka, 1970
  17. Blohincev, D.I., Foundations of Quantum Mechanics, GITTL, Moscow, 3rd ed., Vyss. Skola, Kiev, 1961; English Transl., Reidel, Dordrecht, 1964
  18. Yilmazer, R., N  Fractional Calculus Operator N  Method to a Modified Hydrogen Atom Equation, Math. Commun., 15 (2010), 489-501
  19. Panakhov, E.S., Yilmazer, R., A Hochstadt-Lieberman Theorem for the Hydrogen Atom Equation, Appl. Comp. Math. 11 (2012), 74-80
  20. Bas, E., et al., The Uniqueness Theorem for Hydrogen Atom Equation, TWMS J. Pure Appl. Math. 4 (2013), 20-28

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