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.
[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
[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
Ahmad, M., Bhat, A. A., & Jain, R. (2018). Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method. Journal of New Theory(22), 73-81.
AMA
Ahmad M, Bhat AA, Jain R. Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method. JNT. March 2018;(22):73-81.
Chicago
Ahmad, Manzoor, Altaf Ahmad Bhat, and Renu Jain. “Space Time Fractional Telegraph Equation and Its Application by Using Adomian Decomposition Method”. Journal of New Theory, no. 22 (March 2018): 73-81.
EndNote
Ahmad M, Bhat AA, Jain R (March 1, 2018) Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method. Journal of New Theory 22 73–81.
IEEE
M. Ahmad, A. A. Bhat, and R. Jain, “Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method”, JNT, no. 22, pp. 73–81, March 2018.
ISNAD
Ahmad, Manzoor et al. “Space Time Fractional Telegraph Equation and Its Application by Using Adomian Decomposition Method”. Journal of New Theory 22 (March 2018), 73-81.
JAMA
Ahmad M, Bhat AA, Jain R. Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method. JNT. 2018;:73–81.
MLA
Ahmad, Manzoor et al. “Space Time Fractional Telegraph Equation and Its Application by Using Adomian Decomposition Method”. Journal of New Theory, no. 22, 2018, pp. 73-81.
Vancouver
Ahmad M, Bhat AA, Jain R. Space Time Fractional Telegraph Equation and its Application by Using Adomian Decomposition Method. JNT. 2018(22):73-81.