
AIMS Mathematics, 2019, 4(6): 16641683. doi: 10.3934/math.2019.6.1664.
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Solution of fractional telegraph equation with Riesz spacefractional derivative
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
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Keywords: Riesz space fractional derivative; fractional telegraph equation; fractional derivatives; generalized differential transform method; differential transform method
Citation: S. Mohammadian, Y. Mahmoudi, F. D. Saei. Solution of fractional telegraph equation with Riesz spacefractional derivative. AIMS Mathematics, 2019, 4(6): 16641683. doi: 10.3934/math.2019.6.1664
References:
 1. D. Baleanu, J. H. Asad, A. Jajarmi, The fractional model of spring pendulum: new features within different kernels, Proceeding of the Romanian Academy Series A, 19 (2018), 447454.
 2. M. Hajipour, A. Jajarmi, D. Baleanu, et al. On a accurate discretization of a variableorder fractional reactiondiffusion equation, Commun. Nonlinear Sci., 69 (2019), 119133.
 3. S. S. Sajjadi, A. Jajarmi, J. H. Asad, New features of the fractional EulerLagrange equations for a physical system within nonsingular derivative operator, Eur. Phys. J. Plus, 134 (2019), 181.
 4. D. Baleanu, A. Jajarmi, J. H. Asad, Classical and fractional aspects of two coupled pendulums, Rom. Rep. Phys., 71 (2019), 103115.
 5. S. Kumar, A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model., 38 (2014), 31543163.
 6. D. Kumar, J. Singh, S. kumar, Analytic and approximate solutions of spacetime fractional telegraph equation via Laplace transform, Walailak Journal of Science and Technology (WJST), 11 (2013), 711728.
 7. Z. Zhao, C. Li, Fractional difference/finite element approximations for timespace fractional telegraph equation, Appl. Math. Comput., 219 (2012), 29752988.
 8. Q. Yang, F. liu, I. Turner, Numerical methods for fractional partial differential equations with Riesz space fractional derivatives, Appl. Math. Model., 34 (2010), 200218.
 9. A. H. Bhrawy, M. Zaky, J. A. Tenreiro Machado, Numerical solution of the twosided spacetime fractional telegraph equation via Chebyshev Tau approximation, J. Optimiz. Theory Appl., 174 (2017), 321341.
 10. V. R. Hossieni, W. Chen, Z. Avazzadeh, Numerical solution of fractional telegraph equation by using radial basis functions, Eng. Anal. Bound. Elem., 38 (2014), 3139.
 11. T. Breiten, V. Simoncini, M. Stoll, Lowrank solvers for fractional differential equations, Electron. T. Numer. Anal., 45 (2016), 107132.
 12. J. K. Zhou, Differential Transformation and Its Application for Electrical Circuits, Wuhan, China: Huazhong University Press, 1986.
 13. C. K. Chen, S. H. Ho, Solving partial differential equations by twodimensional differential transform method, Appl. Math. Comput., 106 (1999), 171179.
 14. Z. Odibat, S. Momani, V. S. Erturk, Generalized differential transform method: Application to differential equations of fractional order, Appl. Math. Comput., 197 (2008), 467477.
 15. Z. Odibat, S. Momani, A generalized differential transform method for linear partial differential equations of fractional order, Appl. Math. Lett., 21 (2008), 194199.
 16. S. S. Ray, Numerical solution and solitary wave solutions of fractional KDV equations using modified fractional reduced differnatial transform method, Computational Mathematics and Mathematical Physics, 53 (2013), 18701881.
 17. E. F. D. Goufo, S. Kumar, Shallow water wave models with and without singular kernel:existenc, uniqueness, and similarities, Math. Probl. Eng., 2017 (2017), 19.
 18. B. Soltanalizadeh, differential transform method for solving onespacedimensional telegraph equation, Comput. Appl. Math., 30 (2011), 639653.
 19. V. K. Sirvastava, M. K. Awasthi, R. K. Chaurasia, Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations, Journal of King Saud University: Engineering Sciences, 29 (2017), 166171.
 20. M. Garg, P. Manohar, S. L. Kalla, Generalized differential transform method to space time fractional telegraph equation, International Journal of Differential equations, 2011 (2011), 19.
 21. A. Cetinkaya, O. Kiymaz, The solution of the timefractional diffusion equation by the generalize differential transform method, Math. Comput. Model., 57 (2013), 23492354.
 22. L. Zou, Z. Wang, Z. Zong, Generalized differential transform method to differentialdifference equation, Phys. Lett. A, 373 (2009), 41424151.
 23. J. Biazar, M. Eslami, Analiytic solution of Telegraph equation by differential transform method, Phys. Lett. A, 374 (2010), 29042906.
 24. I. Podlubny, Fractional Differential Equations, SanDiego: Academic Press, 1999.
 25. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, New York: John Wiley & Sons Inc., 1993.
 26. Z. M. Odibat, S. Kumar, N. Shawagfeh, et al. A study on the convergence conditions of generalized differential transform method, Math. Method. Appl. Sci., 40 (2017), 4048.
 27. S. Chen, X. Jiang, F. Liu, et al. High order unconditionally stable difference schemes for the Riesz spacefractional telegraph equation, J. Comput. Appl. Math., 278 (2015), 119129.
 28. Y. Zhang, H. Ding, Improved matrix transform method for the Riesz space fractional reaction dispersion equation, J. Comput. Appl. Math., 260 (2014), 266280.
 29. G. A. Anastassiou, I. K. Argyros, S. Kumar, Monotone convergence of extended iterative methods and fractional calculus with applications, Fund. Inform., 151 (2017), 241253.
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