Korean J. Math. Vol. 27 No. 3 (2019) pp.581-594
DOI: https://doi.org/10.11568/kjm.2019.27.3.581

Some applications for generalized fractional operators in analytic functions spaces

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Published: Sep 30, 2019
Keywords:
Analytic functions, Normalized functions, Srivastava-Owa fractional operators, Generalized Gauss hypergeometric function, Bloch space
Mathematics Subject Classification:
30C45, 30C55

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Adem Kilicman
Department of Mathematics and Institute for Mathematical Research Universiti Putra Malaysia 43400 UPM Serdang, Selangor, Malaysia
Zainab E Abdulnaby
Department of Mathematics College of Science Mustansiriyah University Baghdad, Iraq

Abstract

In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.


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Supporting Agencies

University Putra Malaysia

References

[1] H. M. Srivastava, M. Saigo and S. A. Owa, Class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl. 131 (1988), 412– 420. Google Scholar

[2] H. M. Srivastava, An application of the fractional derivative, Math. Japon. 29 (1984), 383–389. Google Scholar

[3] R. W. Ibrahim, On generalized Srivastava-Owa fractional operators in the unit disk, Adv. Diff. Equa. 55 (2011), 1–10. Google Scholar

[4] A. Kılıc ̧man, R. W. Ibrahim and Z. E. Abdulnaby, On a generalized fractional integral operator in a complex domain, Appl. Math. Inf. Sci. 10 (2016), 1053– 1059. Google Scholar

[5] H. M. Srivastava, P. Agarwal and S. Jain, Generating functions for the general- ized Gauss hypergeometric functions, Appl. Math. Comput. 247 (2014), 348–352. Google Scholar

[6] R. K. Parmar, A new generalization of gamma, beta hypergeometric and confluent hypergeometric functions, Le Matematiche 68 (2013), 33–52. Google Scholar

[7] E. O ̈zergin, Some properties of hypergeometric functions, Ph.D. thesis, Eastern Mediterranean University (EMU), (2011). Google Scholar

[8] H. M. Srivastava, R. K. Parmar and P. A. Chopra, class of extended fractional derivative operators and associated generating relations involving hypergeometric functions, Axioms 1 (2012), 238–258. Google Scholar

[9] M. A. Chaudhry, A. Qadir, M. Rafique and S. Zubair, Extension of euler’s beta function, Appl. Comput. J. 78 (1997), 19–32. Google Scholar

[10] H. M. Srivastava, M. A. Chaudhry and R. P. Agarwal, The incomplete pochhammer symbols and their applications to hypergeometric and related functions, Integ. Trans. Spec F. 23 ( 2012), 659–683. Google Scholar

[11] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach Science Publishers, Yverdon (1993), Translated from the 1987 Russian original. Google Scholar

[12] Z. E. Abdulnaby, R. W. Ibrahim and A. Kılıc ̧man, Some properties for integro differential operator defined by a fractional formal, SpringerPlus 5 (2016), 1–9. Google Scholar

[13] R. W. Ibrahim, A. Kılı ̧cman and Z. E. Abdulnaby, Boundedness of fractional differential operator in complex spaces, Asian-European Journal of Mathematics 10 (2017), 1–12. Google Scholar

[14] Z. E. Abdulnaby, R. W. Ibrahim and A. Kılıc ̧man, On boundedness and compactness of a generalized Srivastava–Owa fractional derivative operator, J. King Saud Univ. Sci. 30 (2018), 153–157. Google Scholar

[15] S. Ruscheweyh, Convolutions in geometric function theory, Fundamental Theories of Physics 83 (1982), MR 674296. Google Scholar

[16] H. M. Srivastava, Some fox-wright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Disc. Math. 1 (2007), 56–71 Google Scholar