Fractional incompressible stars

  • Selcuk S. Bayin
  • Jean P. Krisch
Original Article


In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions and/or stress conditions. To better understand the fractional effects, we discuss effective values for the density and equation of state. The fractional objects are smaller and less massive than integer models. The fractional parameters are related to a polytropic index for the models considered.


Fractional stars Compact objects Incompressible matter Dense matter Equation of state Gravitation 


  1. Abbas, G., Kanwal, A., Zubair, M.: Astrophys. Space Sci. 357, 109 (2015) CrossRefADSGoogle Scholar
  2. Bayin, S.S.: Mathematical Methods in Science and Engineering. Wiley, New York (2006) CrossRefzbMATHGoogle Scholar
  3. Bredberg, I., Keeler, C., Lysov, V., Strominger, A.: (2011). arXiv:1101.2451 [hep-th]
  4. Chandrasekhar, S.: An Introduction to the Study of Stellar Structure. Dover, New York (1939) Google Scholar
  5. El-Nabulsi, R.A.: Appl. Math. Comput. 218, 2837 (2011) MathSciNetCrossRefzbMATHGoogle Scholar
  6. Fiziev, P.P.: Proceedings of the International Conference Days on Diffraction, pp. 76–79 (2014). arXiv:astro-ph/0409458 Google Scholar
  7. Herrmann, R.: Fractional Calculus: An Introduction for Physicists, p. 42. World Scientific, Singapore (2011) CrossRefGoogle Scholar
  8. Hilfer, R. (ed.): Fractional Calculus: Applications in Physics. World Scientific, Singapore (2000) Google Scholar
  9. Huang, T.-Z., Ling, Y., Pan, W.-J., Tian, Y., Wu, X.-N.: J. High Energy Phys. 1110, 079 (2011). arXiv:1107.1464 MathSciNetCrossRefADSGoogle Scholar
  10. Kalam, M., Usmai, A.A., Rahama, F., Hussei, S.M., Karar, I., Sharma, R.: Int. J. Theor. Phys. 52, 3319 (2013) CrossRefzbMATHGoogle Scholar
  11. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) zbMATHGoogle Scholar
  12. Laskin, N.: Phys. Rev. E 62, 3135 (2000) CrossRefADSGoogle Scholar
  13. Lattimer, J.M., Steiner, A.W.: Eur. Phys. J. 50, 40 (2014) CrossRefADSGoogle Scholar
  14. Lysov, V., Strominger, A.: (2011). arXiv:1104.5502 [hep-th]
  15. Mak, M.K., Harko, T.: Eur. Phys. J. C 73, 2585 (2013) CrossRefADSGoogle Scholar
  16. Matsuo, Y., Natsuume, M., Ohta, M., Okamura, T.: (2013). arXiv:1206.6924 [hep-th]
  17. Momeni, D., Gholizade, H., Raza, M., Myrzakulov, R.: (2015a). arXiv:1502.05000
  18. Momeni, D., Moraes, P.H.R.S., Gholizade, H., Myrzakulov, R.: (2015b). arXiv:1505.05113
  19. Oldham, K.B., Spanier, J.: The Fractional Calculus. Dover, New York (1974) zbMATHGoogle Scholar
  20. Olson, T.S.: Phys. Rev. C 63, 015802 (2000) CrossRefADSGoogle Scholar
  21. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999) zbMATHGoogle Scholar
  22. Sandin, F.: Eur. Phys. J. C 40, 15 (2005) CrossRefADSGoogle Scholar
  23. Shapiro, S.S., Teukolsky, S.A.: Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects, p. 71. Wiley, New York (1983) CrossRefGoogle Scholar
  24. Sokolov, I.M., Klafter, J., Blumen, A.: Phys. Today 55, 48 (2002) CrossRefGoogle Scholar
  25. Taniguchi, K., Shibata, M.: Phys. Rev. D 58, 084012 (1998) CrossRefADSGoogle Scholar
  26. Visser, M., Barcelo, C., Liberati, S., Sonego, S.: PoS BHs, GRandStrings 2008:010, 2008; 2009. arXiv:0902.0346
  27. Weber, F.: Prog. Part. Nucl. Phys. 54, 193 (2005) CrossRefADSGoogle Scholar
  28. Zeldovich, Ya.B., Novikov, I.D.: Relativistic Astrophysics, vol. 1 Stars and Relativity. Chicago Press, Chicago (1971) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of PhysicsUniversity of MichiganAnn ArborUSA

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