The Analytical Solution of Telegraph Equation of Space-Fractional Order Derivative by the Aboodh Transform Method
Main Article Content
In this article, an analytical solution based on the series expansion method is proposed to solve the telegraph equation of space - fractional order (TESFO), namely the Aboodh transformation method (ATM) subjected to the appropriate initial condition. Using ATM, it is possible to find exact solution or a closed approximate solution of a differential equation. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.
- S. Kumar. A new analytical modelling for fractional telegraph equation via Laplace transform. Appl. Math. Model. 38 (13) (2014), 3154-3163.
- S. Momani. Analytic and approximate solutions of space and time fractional telegraph equations. Appl. Math. Comput., 170 (2005), 1126-1134.
- A. Yildirim. He's homotopy perturbation method for solving the space- and time-fractional telegraph equations. Int. J. Comput. Math. 87 (13) (2010), 2998-3006.
- M. ELARBI BENATTIA, K. BELGHABA. Numerical Solution for Solving Fractional Differential Equations using Shifted Chebyshev Wavelet. Gen. Lett. Math. 3 (2) (2017), 101-110.
- Mohammed G. S. AL-Safi, Wurood R. Abd AL-Hussein, Ayad Ghazi Naser Al-Shammari. A new approximate solution for the Telegraph equation of space-fractional order derivative by using Sumudu method. Iraqi J. Sci. 59 (3A) (2018), 1301-1311.
- Mohammed AL-Safi, G.S., Farah,L.J. and Muna, S.A. Numerical Solution for Telegraph Equation of Space Fractional Order using Legendre Wavelets Spectral tau Algorithm, Aust. J. Basic Appl. Sci. 10 (12) (2016), 383-391.
- Gupta, V.G., Sharma, B. and Kilicman, A. A Note on Fractional Sumudu Transform. Journal of Applied Mathematics, 2010 (2010), Article ID 154189.
- Sunil, K. 2013. A New Analytical Modelling for Fractional Telegraph Equation Via Laplace Transform. Appl. Math. Model. 38 (13) (2014), 3154-3163.
- Abdelbagy A. Alshikh, Mohand M. Abdelrahim Mahgob. A Comparative Study Between Laplace Transform and Two New Integrals “ELzaki” Transform and “Aboodh” Transform. Pure Appl. Math. J. 5 (5) (2016), 145-150.