Skip to main content
SpringerLink
Log in

Some properties of certain extended fractional differintegral operator

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

Abstract

In this paper, we derive some inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results involving certain extended fractional differintegral operator.

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.

Similar content being viewed by others

References

  1. 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, 545–560 (2016)

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  3. Liu, J.-L.: On a sublcass of multivalent anlytic functions associated with an extended fractional differintegral operator. Bull. Iran. Math. Soc. 39, 107–124 (2013)

    Google Scholar 

  4. Liu, J.-L., Patel, J.: Certain properties of multivalent functions associated with an extended fractional differintegral operator. Appl. Math. Comput. 203, 703–713 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Miller, S.S., Mocanu, P.T.: On some classes of first order differential subordinations. Mich. Math. J. 32, 185–195 (1985)

    Article  MathSciNet  Google Scholar 

  6. Miller, S.S., Mocanu, P.T.: Differential Subordinations, Theory and Applications. Monographs and Textbooks in Pure and Applied Mathematics, vol. 225. Marcel Dekker Inc., New York (2000)

    Google Scholar 

  7. Miller, S.S., Mocanu, P.T.: Subordinats of differential superordinations. Complex Var. Theory Appl. 48, 815–826 (2003)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Shanmugam, T.N., Ravichandran, V., Sivasubramanian, S.: Differential sandwich theorems for subclasses of analytic functions. Aust. J. Math. Anal. Appl. 3, 11 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Sharma, P., Raina, R.K., Sǎlǎgean, G.S.: Some geometric properties of analytic functions involving a new fractional operator. Mediterr. J. Math. 13, 4591–4605 (2016)

    Article  MathSciNet  Google Scholar 

  11. Srivastava, H.M., Owa, S. (eds.): Current Topics in Analytic Function Theory. World Scientific Publishing Co. Inc., River Edge (1992)

    MATH  Google Scholar 

  12. Srivastava, H.M., Sharma, P., Raina, R.K.: Inclusion results for certain classes of analytic functions associated with a new fractional differintegral operator. Rev. R. Acad. Cienc. Exactas Fís. Nat. A. (2017). doi:10.1007/s13398-017-0377-8

    Article  MathSciNet  Google Scholar 

  13. Stankiewicz, J., Stankiewicz, Z.: Some applications of the Hadamard convolution in the theory of functions. Ann. Univ. Mariae Curie Skłodowska A 40, 251–265 (1986)

    MathSciNet  MATH  Google Scholar 

  14. Supramaniam, S., Chandrashekar, R., Lee, S.K., Subramanian, K.G.: Convexity of functions defined by differential inequalities and integral operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. A 111, 147–157 (2017)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The present investigation was supported by the Natural Science Foundation of Hunan Province under Grant No. 2016JJ2036. The authors would like to thank the referees for their valuable suggestions, which improved the quality of this paper.

Author information

Authors and Affiliations

  1. School of Mathematics and Computing Science, Hunan First Normal University, Changsha, 410205, Hunan, People’s Republic of China

    Zhi-Gang Wang

  2. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, Henan, People’s Republic of China

    Lei Shi

Authors
  1. Zhi-Gang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Gang Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, ZG., Shi, L. Some properties of certain extended fractional differintegral operator. RACSAM 112, 993–1003 (2018). https://doi.org/10.1007/s13398-017-0404-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13398-017-0404-9

Keywords

Mathematics Subject Classification

Search

Navigation