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Year 2019, Volume: 2 Issue: 3, 201 - 204, 30.12.2019

Abstract

References

  • [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

Year 2019, Volume: 2 Issue: 3, 201 - 204, 30.12.2019

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

References

  • [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.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Resat Yilmazer 0000-0002-5059-3882

Gonul Oztas This is me 0000-0002-5059-3882

Publication Date December 30, 2019
Acceptance Date December 12, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

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. December 2019;2(3):201-204.
Chicago Yilmazer, Resat, and Gonul Oztas. “Solutions of Singular Differential Equations by Means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 201-4.
EndNote Yilmazer R, Oztas G (December 1, 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 and G. Oztas, “Solutions of Singular Differential Equations by means of Discrete Fractional Analysis”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 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 (December 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 and Gonul Oztas. “Solutions of Singular Differential Equations by Means of Discrete Fractional Analysis”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 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.