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BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 3, 201 - 204, 30.12.2019

Öz

Kaynakça

  • [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] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • [3] C. Goodrich, A. C. Peterson, Discrete Fractional Calculus, Berlin: Springer, 2015.
  • [4] R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [5] H. L., Gray, N., Zhang, On a New Definition of the Fractional Difference, Mathematics of Computation, 50 (182) (1988), 513-529.
  • [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] N. Acar, F. M. Atici, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete Math. 7 (2013), 343-353.
  • [8] G. A. Anastassiou, Right nabla discrete fractional calculus, Int. J. Difference Equations, 6 (2011), 91-104.
  • [9] J. J. Mohan, Analysis of nonlinear fractional nabla difference equations, Int. J. Analysis Applications 7 (2015), 79-95.
  • [10] R. Yilmazer, et al., Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator, Entropy, 18 (49) (2016), 1-6.
  • [11] R. Yilmazer, O. Ozturk, On Nabla Discrete Fractional Calculus Operator for a Modified Bessel Equation, Therm. Sci., 22 (2018), S203-S209.
  • [12] R. Yilmazer, Discrete fractional solution of a Hermite Equation, Journal of Inequalities and Special Functions, 10 (1) (2019), 53-59.
  • [13] R. Yilmazer, Discrete fractional solution of a non-homogeneous non-fuchsian differential equations, Therm. Sci., 23 (2019), 121-127.
  • [14] R. Yilmazer, $N-$fractional calculus operator ${{N}^{\mu }}$ method to a modified hydrogen atom equation, Math. Commun., 15 (2010), 489-501.
  • [15] W. G. Kelley, A. C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, 2001.

Solutions of Singular Differential Equations by means of Discrete Fractional Analysis

Yıl 2019, Cilt: 2 Sayı: 3, 201 - 204, 30.12.2019

Öz

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 ${{\nabla }^{\upsilon }}(0<\upsilon <1).$

Kaynakça

  • [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] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • [3] C. Goodrich, A. C. Peterson, Discrete Fractional Calculus, Berlin: Springer, 2015.
  • [4] R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [5] H. L., Gray, N., Zhang, On a New Definition of the Fractional Difference, Mathematics of Computation, 50 (182) (1988), 513-529.
  • [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] N. Acar, F. M. Atici, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete Math. 7 (2013), 343-353.
  • [8] G. A. Anastassiou, Right nabla discrete fractional calculus, Int. J. Difference Equations, 6 (2011), 91-104.
  • [9] J. J. Mohan, Analysis of nonlinear fractional nabla difference equations, Int. J. Analysis Applications 7 (2015), 79-95.
  • [10] R. Yilmazer, et al., Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator, Entropy, 18 (49) (2016), 1-6.
  • [11] R. Yilmazer, O. Ozturk, On Nabla Discrete Fractional Calculus Operator for a Modified Bessel Equation, Therm. Sci., 22 (2018), S203-S209.
  • [12] R. Yilmazer, Discrete fractional solution of a Hermite Equation, Journal of Inequalities and Special Functions, 10 (1) (2019), 53-59.
  • [13] R. Yilmazer, Discrete fractional solution of a non-homogeneous non-fuchsian differential equations, Therm. Sci., 23 (2019), 121-127.
  • [14] R. Yilmazer, $N-$fractional calculus operator ${{N}^{\mu }}$ method to a modified hydrogen atom equation, Math. Commun., 15 (2010), 489-501.
  • [15] W. G. Kelley, A. C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, San Diego, 2001.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Resat Yilmazer 0000-0002-5059-3882

Gonul Oztas Bu kişi benim 0000-0002-5059-3882

Yayımlanma Tarihi 30 Aralık 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.
AMA Yilmazer R, Oztas G. Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology. Aralık 2019;2(3):201-204.
Chicago Yilmazer, Resat, ve Gonul Oztas. “Solutions of Singular Differential Equations by Means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology 2, sy. 3 (Aralık 2019): 201-4.
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 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, 2019.
ISNAD Yilmazer, Resat - Oztas, Gonul. “Solutions of Singular Differential Equations by Means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology 2/3 (Aralık 2019), 201-204.
JAMA 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, 2019, ss. 201-4.
Vancouver Yilmazer R, Oztas G. Solutions of Singular Differential Equations by means of Discrete Fractional Analysis. Conference Proceedings of Science and Technology. 2019;2(3):201-4.