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Solutions of Singular Differential Equations by means of Discrete Fractional Analysis

Cilt: 2 Sayı: 3 30 Aralık 2019
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Solutions of Singular Differential Equations by means of Discrete Fractional Analysis

Abstract

Recently, many researchers demonstrated the usefulness of fractional calculus in the derivation of particular solutions of linear ordinary and partial differential equation of the second order. In this study, we acquire new discrete fractional solutions of singular differential equations (homogeneous and nonhomogeneous) by using discrete fractional nabla operator ${{\nabla }^{\upsilon }}(0<\upsilon <1).$

Keywords

Kaynakça

  1. [1] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc., New York, 1993.
  2. [2] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  3. [3] C. Goodrich, A. C. Peterson, Discrete Fractional Calculus, Berlin: Springer, 2015.
  4. [4] R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  5. [5] H. L., Gray, N., Zhang, On a New Definition of the Fractional Difference, Mathematics of Computation, 50 (182) (1988), 513-529.
  6. [6] F. M. Atici, P.W. Eloe, Discrete fractional calculus with the nabla operator, Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed I, 3 (2009), 1-12.
  7. [7] N. Acar, F. M. Atici, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete Math. 7 (2013), 343-353.
  8. [8] G. A. Anastassiou, Right nabla discrete fractional calculus, Int. J. Difference Equations, 6 (2011), 91-104.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Konferans Bildirisi

Yayımlanma Tarihi

30 Aralık 2019

Gönderilme Tarihi

25 Eylül 2019

Kabul Tarihi

12 Aralık 2019

Yayımlandığı Sayı

Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA
Yilmazer, R., & Oztas, G. (2019). Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology, 2(3), 201-204. https://izlik.org/JA59XW54KP
AMA
1.Yilmazer R, Oztas G. Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology. 2019;2(3):201-204. https://izlik.org/JA59XW54KP
Chicago
Yilmazer, Resat, ve Gonul Oztas. 2019. “Solutions of Singular Differential Equations by means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology 2 (3): 201-4. https://izlik.org/JA59XW54KP.
EndNote
Yilmazer R, Oztas G (01 Aralık 2019) Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology 2 3 201–204.
IEEE
[1]R. Yilmazer ve G. Oztas, “Solutions of Singular Differential Equations by means of Discrete Fractional Analysis”, Conference Proceedings of Science and Technology, c. 2, sy 3, ss. 201–204, Ara. 2019, [çevrimiçi]. Erişim adresi: https://izlik.org/JA59XW54KP
ISNAD
Yilmazer, Resat - Oztas, Gonul. “Solutions of Singular Differential Equations by means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology 2/3 (01 Aralık 2019): 201-204. https://izlik.org/JA59XW54KP.
JAMA
1.Yilmazer R, Oztas G. Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology. 2019;2:201–204.
MLA
Yilmazer, Resat, ve Gonul Oztas. “Solutions of Singular Differential Equations by means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology, c. 2, sy 3, Aralık 2019, ss. 201-4, https://izlik.org/JA59XW54KP.
Vancouver
1.Resat Yilmazer, Gonul Oztas. Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology [Internet]. 01 Aralık 2019;2(3):201-4. Erişim adresi: https://izlik.org/JA59XW54KP