Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method

Year 2018, Issue: 22, 73 - 81, 26.03.2018

Manzoor Ahmad Altaf Ahmad Bhat , Renu Jain

https://izlik.org/JA74UR42LU

Abstract

The telegraph equations are a pair of linear differential equations which describe the voltage and
current on an electrical transmission line with distance and time. In this paper the authors give a brief
overview of fractional calculus and extend its application to space-time fractional telegraph equation by using
Adomian decomposition method. The time- space derivates are considered as Caputo fractional derivate. The
solutions are obtained in the series form. 

Keywords

Adomian decomposition method , time-space fractional telegraph equation

References

• [1] A. A. Kilbas, H. M. Srivastava & J. J. Trujillo, (2006), Theory and Applications of Fractional Differential Equations: Elsevier, Amsterdam, The Netherlands.
• [2] W. Tomasi, (2004), Electronic Communication Systems, Prentice Hall, New Jersey.
• [3] R. C. Cascaval, E. C. Eckstein, L. Frota & J. A. Goldstein , (2002), Fractional Telegraph Equations: J Math. Anal. Appl., 276, 145-159.
• [4] E. Orsingher & L. Beghin, (2004), Time Fractional Telegraph Equation and Telegraph Process with Brownian Time: Prob. Theory Relat. Fields, 128, 141-160.
• [5] J. Chen, F. Liu & V. Anh, (2008), Analytical Solution for the Time-Fractional Telegraph Equation by the method of Separating Variables: J. Math. Anal. Appl., 338, 1364-1377.
• [6] S. Momani, (2005), Analytic and Approximate solutions of the space and time fractional telegraph equations: Appl. Math. Comput., 170, 1126-1134.
• [7] G. Adomian, (1986), Non-linear Stochastic Operator Equations: Academic Press, San Diego.
• [8] G. Adomian, (1994), Solving Frontier Problems of Physics: The Decomposition Method: Kluwer Acad. Pub., Boston.
• [9] G. Adomian, (1988), A Review of the Decomposition Method in Applied Mathematics: J. Math. Anal. Appl. 135, 501-544.
• [10] A. M. Wazwaz, (2008), A Study on Linear and Nonlinear Schrodinger equations by the Variational Iteration method: Chaos, Solitons and Fractals 37, 1136-1142.
• [11] X. G. Luo, (2005), A two step Adomian decomposition method: Appl. Math Comput. 170(1), 570-583.
• [12] B. Q. Zhang, X. G. Luo and Q. B. Wu, (2006), The restrictions and improvement of the Adomian decomposition method: Appl. Math. Comput. 177, 99-104.
• [13] M. Caputo, (1969), Elasticita e Dissipazione: Zanichelli, Bologa, Italy.
• [14] H. Weyl, (1917), Vierteljahrsschr. d. Naturf. Ges.; Zurich, 62, 296–302.
• [15] E. A. Ibijola, B.J. Adegboyegun and O.Y. Halid, (2008), On Adomian decomposition method (ADM) for numerical solutions of ordinary differential equations: Advances in Natural and Applied Sciences, 3(3) 165-169.
• [16] A. Atangana, (2015), On the stability and convergence of the time-fractional variable order telegraph equation: Journal of Computational Physics 293, 104-114.
• [17] M. A. E. Herzallah, (2010), On abstract fractional telegraph equation: J. Comput. Nonlinear Dyn. 5, 5pp.
• [18] P. Zjaung, F. Liv, (2006), Implicit difference approximation for the time fractional diffusion equation: J. Appl. Math Comput., 22, 87-99.
• [19] M. Azreg-Ainov, (2009), A developed new algorithm for evaluating Adomian polynomials: CMES, 42(1) 1-18.
• [20] E. Babolian, A. R. Vahidi and G. H. Asadi Cordshooli, (2005), Solving differential equations by decomposition method: Applied Mathematics and Computation, 167, 1150-115