Skip to main content
SpringerLink
Log in

Sandwich results of p-valent functions defined by a generalized fractional derivative operator with application to vortex motion

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

For p-valent functions associated with new operator, we study different properties of the differential subordination and superordination related to defined linear operator. Also, we obtain sandwich results for p-valent functions connected to this operator. Furthermore, an application to vortex motion are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Ali, R.M., Ravichandran, V., Hussain, K.M., Subramaniant, K.G.: Differential sandwich theorems for certain analytic functions. Far East J. Math. Sci. 15(1), 87–94 (2005)

    MathSciNet  Google Scholar 

  2. Al-Oboudi, F.M.: On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci. 27, 1429–1436 (2004)

    Article  MATH  Google Scholar 

  3. Amsheri, S.M., Zharkova, V.: Differential sandwich theorems of \(p\)-valent functions associated with a certain fractional derivative operator. Kragujevac Math. J. 35(3), 387–398 (2011)

    MathSciNet  MATH  Google Scholar 

  4. Aouf, M.K.: Certain subclasses of multivalent prestarlike functions with negative coefficients. Demonstr. Math. 40(4), 799–814 (2007)

    MathSciNet  MATH  Google Scholar 

  5. Aouf, M.K., Al-Oboudi, F.M., Haidan, M.M.: On some results for \(\lambda -\)spirallike and \(\lambda -\)Robertson functions of complex order. Publ. Inst. Math. Belgrade 77(91), 93–98 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Aouf, M.K., Mostafa, A.O.: On a subclass of \(n-p\)-valent prestarlike functions. Comput. Math. Appl. 55, 851–861 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Aouf, M.K., Bulboacă, T.: Subordination and superordination properties of multivalent functions defined by certain integral operator. J. Franklin Inst. B 347, 641–65 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Aouf, M.K., Mostafa, A.O., Zayed, H.M.: Some characterizations of integral operators associated with certain classes of \(p\)-valent functions defined by the Srivastava–Saigo–Owa fractional differintegral operator. Complex Anal. Oper. Theory 10, 1267–1275 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Aouf, M.K., Mostafa, A.O., Zayed, H.M.: Subordination and superordination properties of \(p\)-valent functions defined by a generalized fractional differintegral operator. Quaest. Math. 39(4), 545–560 (2016)

    Article  MathSciNet  Google Scholar 

  10. Aouf, M.K., Mostafa, A.O., Zayed, H.M.: On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator. Afr. Mat. 28, 99–107 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bulboacă, T.A.: Classes of first-order differential superordinations. Demonstr. Math. 35(2), 287–292 (2002)

    MathSciNet  MATH  Google Scholar 

  12. Bulboacă, T.A.: A class of superordination-preserving integral operators. Indag. Math. (N.S.) 13(3), 301–311 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kamali, M., Orhan, H.: On a subclass of certian starlike functions with negative coefficients. Bull. Korean Math. Soc. 41(1), 53–71 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Miller, S.S., Mocanu, P.T.: Differential subordinations: theory and applications. Series on monographs and textbooks in pure and appl. math., vol. 255. Marcel Dekker, Inc., New York (2000)

    Book  Google Scholar 

  15. Miller, S.S., Mocanu, P.T.: Subordinations of differential superordinations. Complex Var. 48(10), 815–826 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Milne-Thomson, L.M.: Theoretical hydrodynamics. Macmillan, London (1938)

    MATH  Google Scholar 

  17. Mishra, A.K., Panigrahi, T., Mishra, R.K.: Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking. Math. Comput. Model. 57(3–4), 945–962 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mostafa, A.O., Aouf, M.K., Zayed, H.M., Bulboacă, T.: Multivalent functions associated with Srivastava-Saigo-Owa fractional differintegral operator. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM. (2017). https://doi.org/10.1007/s13398-017-0436-1

  19. Mostafa, A.O., Aouf, M.K., Zayed, H.M.: Inclusion relations for subclasses of multivalent functions defined by Srivastava–Saigo–Owa fractional differintegral operator. Afr. Mat. 29, 655–64 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  20. Mostafa, A.O., Aouf, M.K., Zayed, H.M.: Subordinating results for p-valent functions associated with the Srivastava–Saigo–Owa fractional differintegral operator, Afr. Mat. (2018). https://doi.org/10.1007/s13370-018-0582-4

  21. Obradovic, M., Aouf, M.K., Owa, S.: On some results for starlike functions of complex order. Publ. Inst. Math. Belgrad. 46(60), 79–85 (1989)

    MathSciNet  MATH  Google Scholar 

  22. Owa, S.: On the distortion theorems I. Kyungpook. Math. J. 18, 53–59 (1987)

    MathSciNet  MATH  Google Scholar 

  23. Patel, J., Mishra, A.K.: On certain subclasses of multivalent functions associated with an extended fractional differintegral operator. J. Math. Anal. 332, 109–122 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Royster, W.C.: On the univalence of a certain integral. Michigan Math. J. 12, 385–387 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sălăgean, G.S.: Subclasses of univalent functions, Complex analysis—fifth Romanian finnish seminar, part 1 (Bucharest, 1981). 362–372, Lecture Notes in Math. 1013 Springer, Berlin

  26. Shanmugam, T.N., Ravichandran, V., Sivasubramanian, S.: Differential sandwich theorems for some subclasses of analytic functions. Austral. J. Math. Anal. Appl. 3(1), 1–11 (2006)

    MathSciNet  MATH  Google Scholar 

  27. Srivastava, H.M., Aouf, M.K.: A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. I and II. J. Math. Anal. Appl. 171, 1–13 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  28. Srivastava, H.M., Aouf, M.K.: A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients. I and II. J. Math. Anal. Appl. 192, 973–688 (1995)

    MathSciNet  Google Scholar 

  29. Srivastava, H.M., Aouf, M.K.: Some applications of fractional calculus operators to certain subclasses of prestarlike functions with negative coefficients. Computers Math. Appl. 30(1), 53–61 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  30. Srivastava, H.M., Lashin, A.Y.: Some applications of the Briot–Bouquet differential subordination. J. Inequal. Pure Appl. Math. 6(2), 1–7 (2005). (41)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank Professor Teodor Bulboaca and the referees for their valuable suggestions which led to the improvement of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Menofia University, Shebin El Kom, 32511, Egypt

    H. M. Zayed

  2. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    S. A. Mohammadein

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    M. K. Aouf

Authors
  1. H. M. Zayed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Mohammadein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. K. Aouf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. K. Aouf.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zayed, H.M., Mohammadein, S.A. & Aouf, M.K. Sandwich results of p-valent functions defined by a generalized fractional derivative operator with application to vortex motion. RACSAM 113, 1499–1514 (2019). https://doi.org/10.1007/s13398-018-0559-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-018-0559-z

Keywords

Mathematics Subject Classification

Search

Navigation