Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions

References

• S. Abbasbandy, R.A. Van Gorder, and P. Bakhtiari, Reproducing kernel method for the numerical solution of the Brinkman–Forchheimer momentum equation, J. Comput. Appl. Math. 311 (2017), pp. 262–271. doi: 10.1016/j.cam.2016.07.030
   Web of Science ®Google Scholar
• A. Akgül, M.S. Hashemi, M. Inc, and S.A. Raheem, Constructing two powerful methods to solve the Thomas-Fermi equation, Nonlinear Dyn. 87 (2017), pp. 1435–1444. doi: 10.1007/s11071-016-3125-2
   Web of Science ®Google Scholar
• M. Al-Smadi and O.A. Arqub, Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method, Appl. Math. Comput. 291 (2016), pp. 137–148. doi: 10.1016/j.amc.2016.06.002
   Web of Science ®Google Scholar
• E. Babolian, S. Javadi, and E. Moradi, Error analysis of reproducing kernel Hilbert space method for solving functional integral equations, J. Comput. Appl. Math. 300 (2016), pp. 300–311. doi: 10.1016/j.cam.2016.01.008
   Web of Science ®Google Scholar
• B. Boutarfa, A. Akgül, and M. Inc, New approach for the Fornberg–Whitham type equations, J. Comput. Appl. Math. 312 (2017), pp. 13–26. doi: 10.1016/j.cam.2015.09.016
   Web of Science ®Google Scholar
• F.Z. Geng and Z.Q. Tang, Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems, Appl. Math. Lett. 62 (2016), pp. 1–8. doi: 10.1016/j.aml.2016.06.009
   Web of Science ®Google Scholar
• M. Ghasemi and M. Fardi, Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space, Appl. Math. Comput. 268 (2015), pp. 815–831. doi: 10.1016/j.amc.2015.06.012
   Web of Science ®Google Scholar
• M.S. Hashemi, Constructing a new geometric numerical integration method to the nonlinear heat transfer equations, Commun. Nonlinear Sci. Numer. Simul. 22 (2015), pp. 990–1001. doi: 10.1016/j.cnsns.2014.09.026
   Web of Science ®Google Scholar
• M.S. Hashemi and D. Baleanu, Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line, J. Comput. Phys. 316 (2016), pp. 10–20. doi: 10.1016/j.jcp.2016.04.009
   Web of Science ®Google Scholar
• M.S. Hashemi, D. Baleanu, and M. Parto-Haghighi, A lie group approach to solve the fractional Poisson equation, Rom. J. Phys. 60 (2015), pp. 1289–1297.
   Web of Science ®Google Scholar
• M.S. Hashemt, D. Baleanub, M. Parto-Haghighi, and E. Darvisht, Solving the time-fractional diffusion equation using a lie group integrator, Therm. Sci. 19 (2015), pp. 77–83. doi: 10.2298/TSCI15S1S77H
   Web of Science ®Google Scholar
• V.R. Hosseini, W. Chen, and Z. Avazzadeh, Numerical solution of fractional telegraph equation by using radial basis functions, Eng. Anal. Bound. Elem. 38 (2014), pp. 31–39. doi: 10.1016/j.enganabound.2013.10.009
   Web of Science ®Google Scholar
• M. Inc, A. Akgül, and F.Z. Geng, Reproducing kernel Hilbert space method for solving Bratu's problem, Bull. Malays. Math. Sci. Soc. 38 (2015), pp. 271–287. doi: 10.1007/s40840-014-0018-8
   Web of Science ®Google Scholar
• W. Jiang and Y.Z. Lin, Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), pp. 3639–3645. doi: 10.1016/j.cnsns.2010.12.019
   Web of Science ®Google Scholar
• W. Jiang and T. Tian, Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method, Appl. Math. Model. 39 (2015), pp. 4871–4876. doi: 10.1016/j.apm.2015.03.053
   Web of Science ®Google Scholar
• R. Ketabchi, R. Mokhtari, and E. Babolian, Some error estimates for solving Volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math. 273 (2015), pp. 245–250. doi: 10.1016/j.cam.2014.06.016
   Web of Science ®Google Scholar
• S. Kumar, A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model. 38 (2014), pp. 3154–3163. doi: 10.1016/j.apm.2013.11.035
   Web of Science ®Google Scholar
• X.Y. Li and B.Y. Wu, A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations, J. Comput. Appl. Math. 311 (2017), pp. 387–393. doi: 10.1016/j.cam.2016.08.010
   Web of Science ®Google Scholar
• X. Li and C. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal. 47 (2009), pp. 2108–2131. doi: 10.1137/080718942
   Web of Science ®Google Scholar
• M. Mohammadi and R. Mokhtari, A reproducing kernel method for solving a class of nonlinear systems of PDEs, Math. Model. Anal. 19 (2014), pp. 180–198. doi: 10.3846/13926292.2014.909897
   Web of Science ®Google Scholar
• N. Mollahasania, M. Mohseni(Mohseni)Moghadama, and K. Afrooz, A new treatment based on hybrid functions to the solution of telegraph equations of fractional order, Appl. Math. Model. 40 (2016), pp. 2804–2814. doi: 10.1016/j.apm.2015.08.020
   Web of Science ®Google Scholar
• Y.L. Wang, X.J. Cao, and X.N. Li, A new method for solving singular fourth-order boundary value problems with mixed boundary conditions, Appl. Math. Comput. 217 (2011), pp. 7385–7390. doi: 10.1016/j.amc.2011.02.002
   Web of Science ®Google Scholar
• Y.L. Wang and M.J. Du, Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions, Appl. Math. Comput. 219 (2013), pp. 5918–5925. doi: 10.1016/j.amc.2012.12.009
   Web of Science ®Google Scholar
• Y. Wang, L. Su, X. Cao, and X. Li, Using reproducing kernel for solving a class of singularly perturbed problems, Comput. Math. Appl. 61 (2011), pp. 421–430. doi: 10.1016/j.camwa.2010.11.019
   Web of Science ®Google Scholar
• J. Zhao and J. Xiao, Stability and convergence of an effective finite element method for multiterm fractional partial differential equations, Abstr. Appl. Anal. 2013 (2013), pp. 1–10.
   Google Scholar