Numerical Solution of Riesz Fractional Differential Equation via Meshless Method
Yıl 2019,
Cilt: 2 Sayı: 1, 94 - 96, 30.10.2019
Merve İlkhan
,
Emrah Evren Kara
,
Fuat Usta
Öz
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.
Kaynakça
- [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.
Yıl 2019,
Cilt: 2 Sayı: 1, 94 - 96, 30.10.2019
Merve İlkhan
,
Emrah Evren Kara
,
Fuat Usta
Kaynakça
- [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.