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Open Access A

Differential sandwich subordination of convolution operator acting on complex meromorphic functions

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pp. 245–260Vol. 26Issue 2March 2023DOI: 10.47974/JIM-1449XML
Received:
05 Jan 2021
Accepted:
05 Aug 2021
Published Online:
01 Mar 2023
Article type:
A
Language:
EN
Article no.:
JIM-1449
Pages:
245–260

Abstract

In the present study, a new complex convolution operator is introduced in terms of the meromorphic formula of the generalized Mittag-Leffler functions (MLfs), namely R– function. By employing the subordination methodology, appropriate classes of admissible functions are considered as well as the dual features of the third-order(3rd-order) differential subordination and superordination for this new operator are discussed. As a sequel, the sandwich-type outcome is also examined.

Keywords

Subject Classifications

(2010) Primary 30C45Secondary 308033C100

References

[1] L. de-Branges, A proof of Bieberbach Conjecture, Acta Math., 154(1), (1985), 137-152.
[2] M. K. Aouf and T. M. Seoudy, Subclasses of p-valent functions involving a new operator containing the generalized Mittag-Leffler function, Mediterr. J. Math., 15 (181), (2018), 1-19.
[3] F. Ghanim, A. Aljarah and H.F. Al-Janaby, Classes of Analytic Functions Involving a Generalization by the Srivastava-Attiya Operator, J. Physics: Conference Series, 1562 (1), 012005, 2020, 1-14.
[4] K. R. Lang, Astrophysical Formulae, vol. II: in Space, Time, Matter and Cosmology, Springer-Verlag, New York, USA, 3rd edition, 1999.
[5] R. Hilfer, Ed., Applications of Fractional Calculus in Physics, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 2000.
[6] G. Mittag-Leffler, Sur la nouvelle function (),Exa Comptes Rendus de l’Academie des Sciences Paris, 137, 1903, 554-558.
[7] A. Wiman, Über den fundamentalsatz in der teorie der funcktionen (),Exa Acta Math., 29, 1905, 191-201.
[8] T.R. Prabhakar, A singular integral equation with a generalized Mittag Leffler function in the kernel, Yokohama Math. J., 19(1), 1971, 7-15.
[9] H. M. Srivastava and Ž. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, J. Appl. Math. Comput., 211, (2009) 198-210.
[10] H. M. Srivastava, Some families of Mittag-Leffler type functions and associated operators of fractional calculus (survey), TWMS J. Pure Appl. Math. 7, (2016) 123–145.
[11] D. Kumar, J. Choi and H. M. Srivastava, Solution of a general family of fractional kinetic equations associated with the generalized Mittag-Leffler function, Nonlinear Funct. Anal. Appl., 23, (2018) 455-471.
[12] H. M. Srivastava, A. Fernandez and D. Baleanu, Some new fractional-calculus connections between Mittag-Leffler functions, Mathematics, 7, (2019) 1-10.
[13] R. K. Saxena and K. Nishimoto, N-fractional calculus of generalized Mittag-Leffler functions, J. Fract. Calc., 37, (2010), 43-52.
[14] Y. Singh and R. S. Dubey, Fractional calculus operator with generalize k-Mittag-Leffler function, Journal of Interdisciplinary Mathematics, 23:2, (2020), 545-553.
[15] F. Ghanim and H. F. Al-Janaby, An analytical study on Mittag-Leffler–confluent hypergeometric functions with fractional integral operator, Math Meth Appl Sci., (2020), 1-10.
[16] D. Kumar and S. Kumar, Fractional calculus of the generalized Mittag-Leffler type function, International Scholarly Research Notices, 2014, (2014), 1-6.
[17] J. A. Antonion and S. S. Miller, Third-order differential inequalities and subordinations in the complex plane, Complex Var. Elliptic Equ. 56, (2011), 439-454.
[18] H. Tang, H. M. Srivastava, S. Li and L. Ma, Third order differential subordination and superordination results for meromorphically multivalent functions associated with the Liu-Srivastava operator, Abstr. Appl. Anal. 2014, 2014, 1–11.
[19] A. A. Attiya and A. H. Hakami, Some subordination results associated with generalized Srivastava-Attiya operator. Advances in Difference Equations. 105, (2013).
[20] H. Tang, H. M. Srivastava, G. Deng and S. Li, Second-order differential superordination for analytic functions in the upper half-plane. Journal of Nonlinear Sciences and Applications. 10(10), (2017), 5271-5280.

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