Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets


Hossein Jafari1, Hassan Kamil Jassim2

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
2 Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah, Iraq.


Abstract
In this paper, we will compare between the local fractional Adomian decomposition
method (LFADM) and local fractional series expansion method (LFSEM) for solving the
telegraph equation on Cantor sets within local fractional operator. The results obtained
by (LFADM) are compared with the results obtained by (LFSEM). Some examples are
given to illustrate the efficiency and accuracy of the presented methods.
 

Key Words: Fractional telegraph equation; Local fractional Adomian decomposition method; Local fractional series expansion method; Local fractional operators 



References

[1] S. P. Yan, H. Jafari, and H. K. Jassim, " Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, Article ID 161580, pp. 1-7, (2014).
[2] H. Jafari, and H. K. Jassim, "Local Fractional Series Expansion Method for Solving Laplace and Schrodinger Equations on Cantor Sets within Local Fractional Operators", International Journal of Mathematics and Computer Research, Vol. 2, No. 11, pp. 736-744, (2014).
[3] H. Jafari, and H. K. Jassim, " Local Fractional Adomian Decomposition Method for Solving Two Dimensional Heat conduction Equations within Local Fractional Operators", Advance in Mathematics, Vol. 9, No. 4. PP. 2574-2582, (2014).
[4] A. M. Yang, X. J. Yang, and Z. B. Li, " Local Fractional series expansion method for Solving wave and diffusion Equations on Cantor sets," Abstract and Applied Analysis, Article ID 351057, pp. 1-6, (2013).
[5] A. M. Yang, Y. Z. Zhang, C. Cattani, et al., “Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets,” Abstract and Applied Analysis, vol. 2014, Article ID 372741, pp.1-6, (2014).
[6] A. M. Yang, Z. S. Chen, X. J. Yang, " Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Operators", Abstract and Applied Analysis, Article ID 259125, pp. 1-6, (2013).