An approximate solution of fractional cable equation by homotopy analysis method

Boundary Value Problems

Volumn 2014, Issue , 2014, Pages

  Inc, Mustafa ^a   Cavlak, Ebru ^a   Bayram, Mustafa ^b  

^a FIRAT UNIVERSITY   (Turkey)

^b YILDIZ TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Cable equation; Fractional cable equation; Fractional differential equations; Homotopy analysis method

Indexed keywords

EID: 84900301142     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1186/1687-2770-2014-58     Document Type: Article

References (20)

1. Wang, Q: Homotopy perturbation method for fractional KdV equation. Appl. Math. Comput. 190, 1795 (2007)
2. Golmakhaneh, AK, Golmakhaneh, AK, Baleanu, D: On nonlinear fractional Klein-Gordon equation. Signal Process. 91, 446 (2011)
3. Chen, J, Liu, F, Anh, V: Analytical solution for the time fractional telegraph equation by the method of separating variables. J. Math. Anal. Appl. 338, 1364 (2008)
4. Momani, S, Odibat, Z, Alawneh, A: Variational iteration method for solving the space-and time-fractional KdV equation. Numer. Methods Partial Differ. Equ. 24(1), 262 (2008)
5. Momani, S: An explicit and numerical solutions of the fractional KdV equation. Math. Comput. Simul. 70, 110 (2005)
6. Inc, M: On numerical solution of Burgers' equation by homotopy analysis method. Phys. Lett. A 372, 356 (2008)
7. Langlands, TAM, Henry, B, Wearne, S: Solution of a fractional cable equation: Finite case. Preprint, Submitted to Elsevier Science http://www.maths.unsw.edu.au/applied/filed/2005/amr05-33.pdf (2005)
8. Keener, J, Sneyd, J: Mathematical Physiology. Springer, Berlin (1991)
9. Liu, F, Yang, Q, Turner, I: Stability and convergence of two new implicit numerical methods for fractional cable equation. In: Proceeding of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE, San Diego, California, USA (2009)
10. Hu, X, Zhang, L: Implicit compact difference scheme for the fractional cable equation. Appl. Math. Model. 36(9), 4027 (2012)
11. Quintana-Murillo, J, Yuste, SB: An explicit numerical method for the fractional cable equation. Int. J. Differ. Equ. (2011). doi:10.1155/2011/231920
12. Liao, SJ: Beyond Perturbation: Introduction to the Homotopy Analysis Method. Chapman & Hall/CRC, Boca Raton (2003)
13. Inc, M: On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method. Phys. Lett. A 365, 412 (2007)
14. Abbasbandy, S: Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method. Appl. Math. Model. 32, 2706 (2008)
15. Abbasbandy, S, Shivanian, E: Series solution of the system of integro-differential equations. Z. Naturforsch. A 64, 811 (2009)
16. Yinping, L, Zhibin, L: The homotopy analysis method for approximating the solution of the modified Korteweg-de Vries equation. Chaos Solitons Fractals 39, 1 (2009)
17. Jafari, H, Tajadodi, H, Biswas, A: Homotopy analysis method for solving a couple of evolution equations and comparison with Adomian decomposition method. Waves Random Complex Media 21(4), 657-667 (2011)
18. Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204 (2006)
19. Podlubny, I: Fractional Differential Equations. Academic Press, San Diego (1999)
20. Oldham, KB, Spanier, J: The Fractional Calculus. Academic Press, New York (1974)