Certain inequalities of meromorphic univalent functions associated with the Mittag-Leffler function

• Autorzy: Aouf Mohamed K. , Mostafa Adela O.

Identyfikatory

DOI

10.1515/jaa-2019-0018

• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to prove differential inequalities for meromorphic univalent functions by using a new operator associated with the Mittag-Leffler function.

Słowa kluczowe

EN

univalent; Mittag-Leffler function; meromorphic functions; meromorphic operator

PL

funkcja Mittag-Lefflera; funkcje meromorficzne; operatory meromorficzne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 2
• Strony: 173--178
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Aouf Mohamed K.

• Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt

autor

Mostafa Adela O.

• Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt

Bibliografia

• [1] A. Fernandez, D. Baleanu and H. M. Srivastava, Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions, Commun. Nonlinear Sci. Numer. Simul. 67 (2019), 517-527.
• [2] V. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus. Higher transcendental functions and their applications, Comput. Appl. Math. 118 (2000), no. 1-2, 241-259.
• [3] V. Kiryakova, The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus, Comput. Math. Appl. 59 (2010), no. 5, 1885-1895.
• [4] V. Kiryakova, Criteria for univalence of the Dziok-Srivastava and the Srivastava-Wright operators in the class A, Appl. Math. Comput. 218 (2011), no. 3, 883-892.
• [5] S. S. Miller and P. T. Mocanu, Second-order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), no. 2, 289-305.
• [6] G. M. Mittag-Leffler, Sur la nouvelle function, C.R. Acad. Sci. Paris 137 (1903), 554-558.
• [7] G. Mittag-Leffler, Sur la représentation analytique d’une branche uniforme d’une fonction monogène, Acta Math. 29 (1905), no. 1, 101-181, cinquième note.
• [8] H. M. Srivastava, M. Bansal and P. Harjule, A study of fractional integral operators involving a certain generalized multi-index Mittag-Leffler function, Math. Methods Appl. Sci. 41 (2018), no. 16, 6108-6121.
• [9] H. M. Srivastava, B. A. Frasin and V. Pescar, Univalence of integral operators involving Mittag-Leffler functions, Appl. Math. Inf. Sci. 11 (2017), no. 3, 635-641.
• [10] H. M. Srivastava and v. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput. 211 (2009), no. 1, 198-210.
• [11] V. Tomovski, R. Hilfer and H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms Spec. Funct. 21 (2010), no. 11, 797-814.
• [12] V. Tomovski, T. K. Pogány and H. M. Srivastava, Laplace type integral expressions for a certain three-parameter family of generalized Mittag-Leffler functions with applications involving complete monotonicity, J. Franklin Inst. 351 (2014), no. 12, 5437-5454.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).