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Numerical Solution of Riesz Fractional Differential Equation via Meshless Method

Year 2019, Volume: 2 Issue: 1, 94 - 96, 30.10.2019

Merve İlkhan , Emrah Evren Kara , Fuat Usta

Abstract

In this study, we present the numerical solution of Riesz fractional differential equation with the help of meshless method.  In accordance with this purpose, we benefit the radial basis functions (RBFs) interpolation method and conformable fractional calculus. We finally present the results of numerical experimentation to show that presented algorithm provide successful consequences.

Keywords

Numerical solution Fractional calculus RBF interpolation

References

  • [1] U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
  • [2] MD. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge University Press, 2003.
  • [3] W. Cheney and W. Light, A Course in Approximation Theory, William Allan, New York, 1999.
  • [4] Q. Yang., F. Liu, and I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Modelling., 34(200-218) (2010).
  • [5] C. Franke and R. Schaback, Solving partial differential equations by collocation using radial basis functions, Appl. Math. Comput. , 93 (1998) 73-82.
  • [6] E. J. Kansa, Multiquadrics a scattered data approximation scheme with applications to computational filuid-dynamics. I. Surface approximations and partial derivative estimates, Comput. Math. Appl. 19(8-9) (1990) 127-145.

Year 2019, Volume: 2 Issue: 1, 94 - 96, 30.10.2019

Merve İlkhan , Emrah Evren Kara , Fuat Usta

Abstract

References

  • [1] U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
  • [2] MD. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge University Press, 2003.
  • [3] W. Cheney and W. Light, A Course in Approximation Theory, William Allan, New York, 1999.
  • [4] Q. Yang., F. Liu, and I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Modelling., 34(200-218) (2010).
  • [5] C. Franke and R. Schaback, Solving partial differential equations by collocation using radial basis functions, Appl. Math. Comput. , 93 (1998) 73-82.
  • [6] E. J. Kansa, Multiquadrics a scattered data approximation scheme with applications to computational filuid-dynamics. I. Surface approximations and partial derivative estimates, Comput. Math. Appl. 19(8-9) (1990) 127-145.
There are 6 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Merve İlkhan 0000-0002-0831-1474

Emrah Evren Kara 0000-0002-6398-4065

Fuat Usta 0000-0002-7750-6910

Publication Date October 30, 2019
Acceptance Date October 21, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA İlkhan, M., Kara, E. E., & Usta, F. (2019). Numerical Solution of Riesz Fractional Differential Equation via Meshless Method. Conference Proceedings of Science and Technology, 2(1), 94-96.
AMA İlkhan M, Kara EE, Usta F. Numerical Solution of Riesz Fractional Differential Equation via Meshless Method. Conference Proceedings of Science and Technology. October 2019;2(1):94-96.
Chicago İlkhan, Merve, Emrah Evren Kara, and Fuat Usta. “Numerical Solution of Riesz Fractional Differential Equation via Meshless Method”. Conference Proceedings of Science and Technology 2, no. 1 (October 2019): 94-96.
EndNote İlkhan M, Kara EE, Usta F (October 1, 2019) Numerical Solution of Riesz Fractional Differential Equation via Meshless Method. Conference Proceedings of Science and Technology 2 1 94–96.
IEEE M. İlkhan, E. E. Kara, and F. Usta, “Numerical Solution of Riesz Fractional Differential Equation via Meshless Method”, Conference Proceedings of Science and Technology, vol. 2, no. 1, pp. 94–96, 2019.
ISNAD İlkhan, Merve et al. “Numerical Solution of Riesz Fractional Differential Equation via Meshless Method”. Conference Proceedings of Science and Technology 2/1 (October 2019), 94-96.
JAMA İlkhan M, Kara EE, Usta F. Numerical Solution of Riesz Fractional Differential Equation via Meshless Method. Conference Proceedings of Science and Technology. 2019;2:94–96.
MLA İlkhan, Merve et al. “Numerical Solution of Riesz Fractional Differential Equation via Meshless Method”. Conference Proceedings of Science and Technology, vol. 2, no. 1, 2019, pp. 94-96.
Vancouver İlkhan M, Kara EE, Usta F. Numerical Solution of Riesz Fractional Differential Equation via Meshless Method. Conference Proceedings of Science and Technology. 2019;2(1):94-6.
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