Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2019, Cilt: 7 Sayı: 1, 199 - 202, 15.04.2019

Öz

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.

Kaynakça

  • [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.
Yıl 2019, Cilt: 7 Sayı: 1, 199 - 202, 15.04.2019

Öz

Kaynakça

  • [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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Basem Frasin

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 20 Ocak 2018
Kabul Tarihi 18 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

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. Nisan 2019;7(1):199-202.
Chicago Frasin, Basem. “An Application of an Operator Associated With Generalized Mittag-Leffler Function”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 199-202.
EndNote Frasin B (01 Nisan 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., c. 7, sy. 1, ss. 199–202, 2019.
ISNAD Frasin, Basem. “An Application of an Operator Associated With Generalized Mittag-Leffler Function”. Konuralp Journal of Mathematics 7/1 (Nisan 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, c. 7, sy. 1, 2019, ss. 199-02.
Vancouver Frasin B. An Application of an Operator Associated with Generalized Mittag-Leffler Function. Konuralp J. Math. 2019;7(1):199-202.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.