THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Erdal Bas

,

Funda Metin Turk

AN APPLICATION OF COMPARISON CRITERIA TO FRACTIONAL SPECTRAL PROBLEM HAVING COLOUMB POTENTIAL

ABSTRACT
In this study, the zeros of eigen functions of spectral theory are considered in fractional Sturm-Liouville problem. The 1st and 2nd comparison theorems for fractional Sturm-Liouville equation with boundary condition and their proofs are given. In this way, our new approximation will contribute to construct fractional Sturm-Liouville theory. Also, its an application is given in case of Coulomb potential and the results are presented by a symbolic graph.
KEYWORDS
Thermal conduction, Angular momentum, Coulomb potential, Energy equation, Sturm-Liouville, Schrödinger equation
PAPER SUBMITTED: 2017-06-13
PAPER REVISED: 2017-11-14
PAPER ACCEPTED: 2017-11-18
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170612273B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S79 - S85]
REFERENCES
  1. . Johnson, R.S., An introduction to Sturm-Liouville theory, University of Newcastle, 2006.
  2. . Zettl, A., Sturm-Liouville Theory, Mathematical Surveys and Monographs, American Mathematical Society, 2005.
  3. . Amrein, W. O., Hinz, A. M. and Pearson, D. B., Sturm-Liouville Theory: Past and Present, Switzerland: Birkhauser, Basel, 2005.
  4. . Levitan, B. M. and Sargsjan, I.S., Introduction to Spectral Theory: Self adjoint Ordinary Differential Operators, American Math. Soc. Pro. R.I., 1975.
  5. . Panakhov, E.S., On the determination the differential operator pecularity in zero, Dep viniti an sssr, 4407-80 (1980), pp. 1-16.
  6. . Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  7. . Carpinteri, A. and Mainardi, F. (Editors), Fractals and Fractional Calculus in Continum Mechanics, Telos: Springer-Verlag, 1998.
  8. . Podlubny, I., Fractional Differential Equations, USA: Academic Press, San Diego, CA, 1999.
  9. . Samko, S. G., Kilbass, A. A. and Marichev, O. I., Fractional Integrals and Derivatives: Theory and Applications, PA: Gordon and Breach, 1993.
  10. . Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, New York, , Inc., 1993.
  11. . Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Netherlands: Elsevier, Amsterdam, 2006.
  12. . Baleanu, D., Octavian G., M., Agarwal, P. R., Asymptotic integration of (1+alpha)-order fractional differential equations, Computers & Mathematics with Applications, 62-3 (2011), pp. 1492-1500.
  13. . Abolhassan, R., Baleanu, D. Vahid Johari, M., Conditional Optimization Problems: Fractional Order Case, Journal of optimization theory and appl., 156 (2013), pp. 45-55.
  14. . Baleanu, D., Guo-Cheng, W., New applications of the variational iteration method-from differential equations to q-fractional difference equations, Advances in difference eq., 21 (2013), DOI: 10.1186/1687-1847.
  15. . Said Grace, R., Agarwal, R. P., Wong, P. J.Y., Zafer, A., On the oscillation of fractional differential equations, Frac. Calc. App. Anal., 15 (2012), pp. 222-231.
  16. . Klimek, M., On Solutions of Linear Fractional Differential Equations of a Variational Type Czestochowa, The Publishing Office of Czestochowa University of Technology, 2009.
  17. . Bas, E., Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator, Journal of Function Spaces and Applications, (2013), 7 pages, ID 915830.
  18. . Al-Mdallal, Q. M., An efficient method for solving fractional Sturm-Liouville problems, Chaos Solitons and Fractals, 40 (2009), pp. 183-189.
  19. . Erturk, V. S., Computing eigenelements of Sturm-Liouville Problems of fractional order via fractional differential transform method, Mathematical and Computational Applications, 16 (2011), pp. 712-720.
  20. . Klimek, M. and Argawal, O. P., On a Regular Fractional Sturm-Liouville Problem with Derivatives of Order in (0,1), Proceeding, 13 th Int. Cont. Conf., 2012.
  21. . Bas, E., Metin, F., Fractional Singular Sturm-Liouville Operator for Coulomb Potential, Advances in Differences Equations, (2013), doi:10.1186/1687-1847-300-2013.
  22. . Bas, E., Metin, F., Spectral Analysis for Fractional Hydrogen Atom Equation, Advances in Pure Mathematics, 5 (2015), pp. 767-773.
  23. . Klimek, M., Argawal, O. P., Fractional Sturm-Liouville problem, Computers and Mathematics with Applications, 66 (2013), pp.795-812.
  24. . Akano, T. T., Fakinlede, O. A., Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition, International Journal of Mathematical and Computational Sciences, 9 (2015).
  25. . Blohincev, D. I., Foundations of Quantum Mechanics, GITTL, Moscow, 1949.
  26. . Bas, E., and Ozarslan, R. "Sturm-Liouville Problem via Coulomb Type in Difference Equations." Filomat 31.4 (2017), pp.989-998.
PDF VERSION [DOWNLOAD]
An application of comparison criteria to fractional spectral problem having Coloumb potential

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence