Research Article

N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation

Volume: 9 Number: 1 February 1, 2012
EN

N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation

Abstract

By means of fractional calculus techniques, we find explicit solutions of the Gegenbauer equation. We use the N-fractional calculus operator Nη method to derive the solutions of these equations.

Keywords

References

  1. [1] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons 1993.
  2. [2] K. Oldham and J. Spanier, The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order, Mathematics in Science and Engineering V, Academic Press 1974.
  3. [3] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, Methods of Their Solution and Some of Their Applications, Mathematics in Science and Enginering 198, Academic Press, New York, London, Tokyo and Toronto 1999.
  4. [4] B. Ross (Editor), Fractional Calculus and Its Applications: Proceedings of the International Conference Held at the University of New Haven, June 1974, Lecture Notes in Mathematics 457, Springer, New York 1975.
  5. [5] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Translated from the Russian: Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, 1987) Gordon and Breach Science Publishers 1993.
  6. [6] D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York 2012.
  7. [7] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies 204, Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York 2006.
  8. [8] S.-T. Tu, D.-K. Chyan and H. M. Srivastava, Some families of ordinary and partial fractional differintegral equations, Integral Transforms and Special Functions 11 (2001), 291–302.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Ökkeş Öztürk This is me

Publication Date

February 1, 2012

Submission Date

May 1, 2012

Acceptance Date

-

Published in Issue

Year 2012 Volume: 9 Number: 1

APA
Yılmazer, R., & Öztürk, Ö. (2012). N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation. Cankaya University Journal of Science and Engineering, 9(1). https://izlik.org/JA89MD95AS
AMA
1.Yılmazer R, Öztürk Ö. N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation. CUJSE. 2012;9(1). https://izlik.org/JA89MD95AS
Chicago
Yılmazer, Reşat, and Ökkeş Öztürk. 2012. “N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation”. Cankaya University Journal of Science and Engineering 9 (1). https://izlik.org/JA89MD95AS.
EndNote
Yılmazer R, Öztürk Ö (February 1, 2012) N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation. Cankaya University Journal of Science and Engineering 9 1
IEEE
[1]R. Yılmazer and Ö. Öztürk, “N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation”, CUJSE, vol. 9, no. 1, Feb. 2012, [Online]. Available: https://izlik.org/JA89MD95AS
ISNAD
Yılmazer, Reşat - Öztürk, Ökkeş. “N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation”. Cankaya University Journal of Science and Engineering 9/1 (February 1, 2012). https://izlik.org/JA89MD95AS.
JAMA
1.Yılmazer R, Öztürk Ö. N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation. CUJSE. 2012;9. Available at https://izlik.org/JA89MD95AS.
MLA
Yılmazer, Reşat, and Ökkeş Öztürk. “N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation”. Cankaya University Journal of Science and Engineering, vol. 9, no. 1, Feb. 2012, https://izlik.org/JA89MD95AS.
Vancouver
1.Reşat Yılmazer, Ökkeş Öztürk. N-Fractional Calculus Operator Nη Method Applied to a Gegenbauer Differential Equation. CUJSE [Internet]. 2012 Feb. 1;9(1). Available from: https://izlik.org/JA89MD95AS