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An Application of an Operator Associated with Generalized Mittag-Leffler Function

Year 2019, Volume: 7 Issue: 1, 199 - 202, 15.04.2019

Abstract

The main object of this paper is to give an application of an operator associated with generalized Mittag-Leffler function in the unit disk $% \mathcal{U}=\{z\in \mathbb{C}:\left\vert z\right\vert <1\}$ to the differential inequalities.

References

  • [1] A. A. Attiya, Some Applications of Mittag-Leffler Function in the Unit Disk, Filomat 30:7 (2016), 2075–2081.
  • [2] D. Bansal, J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61(3)(2016), 338-350.
  • [3] B. A. Frasin, Starlikeness and convexity of integral operators involving Mittag-Leffler functions, TWMS Journal of Pure and Applied Mathematics, in press.
  • [4] M. Garg, P. Manohar and S.L. Kalla, A Mittag-Leffler-type function of two variables. Integral Transforms Spec. Funct. 24 (2013), no. 11, 934–944.
  • [5] V. Kiryakova, Generalized fractional calculus and applications. Pitman Research Notes in Mathematics Series, 301. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
  • [6] V. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus. Higher transcendental functions and their applications, J. Comput. Appl. Math. 118 (2000), no. 1-2, 241–259.
  • [7] 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.
  • [8] F. Mainardia and R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes. Higher transcendental functions and their applications. J. Comput. Appl. Math. 118 (2000), no. 1-2, 283–299.
  • [9] S. S. Miller and P.T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Ana.Appl. 65(1978), 289-305.
  • [10] G. M. Mittag-Leffler, Sur la nouvelle fonction E(x), C. R. Acad. Sci., Paris, 137(1903), 554-558.
  • [11] H. M. Srivastava, B. A. Frasin and Virgil Pescar, Univalence of Integral Operators Involving Mittag-Leffler Functions, Appl. Math. Inf. Sci. 11, No. 3, 635-641 (2017).
  • [12] H.M. Srivastava and Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comp., 211(2009), 198-210.
  • [13] A. Wiman, Uber den Fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 29(1905), 191-201.
Year 2019, Volume: 7 Issue: 1, 199 - 202, 15.04.2019

Abstract

References

  • [1] A. A. Attiya, Some Applications of Mittag-Leffler Function in the Unit Disk, Filomat 30:7 (2016), 2075–2081.
  • [2] D. Bansal, J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Equ., 61(3)(2016), 338-350.
  • [3] B. A. Frasin, Starlikeness and convexity of integral operators involving Mittag-Leffler functions, TWMS Journal of Pure and Applied Mathematics, in press.
  • [4] M. Garg, P. Manohar and S.L. Kalla, A Mittag-Leffler-type function of two variables. Integral Transforms Spec. Funct. 24 (2013), no. 11, 934–944.
  • [5] V. Kiryakova, Generalized fractional calculus and applications. Pitman Research Notes in Mathematics Series, 301. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
  • [6] V. Kiryakova, Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus. Higher transcendental functions and their applications, J. Comput. Appl. Math. 118 (2000), no. 1-2, 241–259.
  • [7] 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.
  • [8] F. Mainardia and R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes. Higher transcendental functions and their applications. J. Comput. Appl. Math. 118 (2000), no. 1-2, 283–299.
  • [9] S. S. Miller and P.T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Ana.Appl. 65(1978), 289-305.
  • [10] G. M. Mittag-Leffler, Sur la nouvelle fonction E(x), C. R. Acad. Sci., Paris, 137(1903), 554-558.
  • [11] H. M. Srivastava, B. A. Frasin and Virgil Pescar, Univalence of Integral Operators Involving Mittag-Leffler Functions, Appl. Math. Inf. Sci. 11, No. 3, 635-641 (2017).
  • [12] H.M. Srivastava and Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comp., 211(2009), 198-210.
  • [13] A. Wiman, Uber den Fundamental satz in der Theorie der Funcktionen E(x), Acta Math., 29(1905), 191-201.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Basem Frasin

Publication Date April 15, 2019
Submission Date January 20, 2018
Acceptance Date March 18, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Frasin, B. (2019). An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp Journal of Mathematics, 7(1), 199-202.
AMA Frasin B. An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp J. Math. April 2019;7(1):199-202.
Chicago Frasin, Basem. “An Application of an Operator Associated With Generalized Mittag-Leffler Function”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 199-202.
EndNote Frasin B (April 1, 2019) An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp Journal of Mathematics 7 1 199–202.
IEEE B. Frasin, “An Application of an Operator Associated with Generalized Mittag-Leffler Function”, Konuralp J. Math., vol. 7, no. 1, pp. 199–202, 2019.
ISNAD Frasin, Basem. “An Application of an Operator Associated With Generalized Mittag-Leffler Function”. Konuralp Journal of Mathematics 7/1 (April 2019), 199-202.
JAMA Frasin B. An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp J. Math. 2019;7:199–202.
MLA Frasin, Basem. “An Application of an Operator Associated With Generalized Mittag-Leffler Function”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 199-02.
Vancouver Frasin B. An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp J. Math. 2019;7(1):199-202.
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