[1]
|
T. Akram, M. Abbas, A. I. Ismail, N. Hj. M. Ali and D. Baleanu, Extended cubic B-splines in the numerical solution of time fractional telegraph equation, Adv. Differ. Equ., (2019), Paper No. 365, 20 pp.
doi: 10.1186/s13662-019-2296-9.
|
[2]
|
D. J. Arrigo and S. G. Krantz, Analytical Techniques for Solving Nonlinear Partial Differential Equations, Morgan & Claypool Publishers, 2019.
doi: 10.2200/S00907ED1V01Y201903MAS025.
|
[3]
|
A. Atangana, On the stability and convergence of the time-fractional variable order telegraph equation, J. Comput. Phys., 293 (2015), 104-114.
doi: 10.1016/j.jcp.2014.12.043.
|
[4]
|
R. C. Cascaval, E. C. Eckstein, C. L. Frota and J. A. Goldstein, Fractional telegraph equations, J. Math. Anal. Appl., 276 (2002), 145-159.
doi: 10.1016/S0022-247X(02)00394-3.
|
[5]
|
J. Chen, F. Liu and V. Anh, Analytical solution for the time-fractional telegraph equation by the method of separating variables, J. Math. Anal. Appl., 338 (2008), 1364-1377.
doi: 10.1016/j.jmaa.2007.06.023.
|
[6]
|
S. Das, K. Vishal, P. K. Gupta and A. Yildirim, An approximate analytical solution of time-fractional telegraph equation, Appl. Math. Comput., 217 (2011), 7405-7411.
doi: 10.1016/j.amc.2011.02.030.
|
[7]
|
W. Deng and Z. Zhang, High Accuracy Algorithm for the Differentail Equations Governing Anomalous Diffusion, Algorithm and Models for Anomalous Diffusion, World Scientific, Singapore, 2019.
|
[8]
|
K. Diethelm, The Analysis of Fraction Differential Equations, Springer, 2010.
doi: 10.1007/978-3-642-14574-2.
|
[9]
|
M. Ferreira, M. M. Rodrigues and N. Vieira, First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac oprators, Adv. Appl. Clifford Algebr, 28 (2018), Art. 42, 14 pp.
doi: 10.1007/s00006-018-0858-7.
|
[10]
|
N. J. Ford, M. M. Rodrigues, J. Xiao and Y. Yan, Numerical analysis of a two-parameter fractional telegraph equation, J. Comput. Appl. Math., 249 (2013), 95-106.
doi: 10.1016/j.cam.2013.02.009.
|
[11]
|
B. Guo, X. Pu and F. Huang, Fractional Partial Differential Equations and Their Numerical Solutions, Science Press, Beijing, 2011.
doi: 10.1142/9543.
|
[12]
|
L. Hervé and L. Brigitte, Partial Differential Equations: Modeling, Analysis and Numerical Approximation, Springer International Publishing, Switzerland, 2016.
|
[13]
|
M. H. Heydari, M. R. Hooshmandasl and F. Mohammadi, Two-Dimensional legendre wavelets for solving time-fractional telegraph equation, Adv. Appl. Math. Mech., 6 (2014), 247-260.
doi: 10.4208/aamm.12-m12132.
|
[14]
|
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), 31-39.
doi: 10.1016/j.enganabound.2013.10.009.
|
[15]
|
W. Jiang and Y. Lin, Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3639-3645.
doi: 10.1016/j.cnsns.2010.12.019.
|
[16]
|
K. Kumar, R. K. Pandey and S. Yadav, Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms, Physica A, 535 (2019), Art. 122271, 15 pp.
doi: 10.1016/j.physa.2019.122271.
|
[17]
|
C. Li and F. Zeng, Numerical Methods for Fractional Calculus, CRC Press, Boca Raton, 2015.
|
[18]
|
C. Li, Z. Zhao and Y. Chen, Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion, Comput. Math. Appl., 62 (2011), 855-875.
doi: 10.1016/j.camwa.2011.02.045.
|
[19]
|
Y. Lin and C. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225 (2007), 1533-1552.
doi: 10.1016/j.jcp.2007.02.001.
|
[20]
|
F. Liu, P. Zhuang, V. Anh, I. Turner and K. Burrage, Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation, Appl. Math. Comput, 191 (2007), 17-20.
doi: 10.1016/j.amc.2006.08.162.
|
[21]
|
F. Liu, P. Zhuang and Q. Liu, Numerical Solutions of Fractional Order Partial Differential Equations and its Applications, Science Press, Beijing, 2015.
|
[22]
|
M. O. Mamchuev, Solutions of the main boundary value problems for the time-fractional telegraph equation by the green function method, Fract. Calc. Appl. Anal., 20 (2017), 190-211.
doi: 10.1515/fca-2017-0010.
|
[23]
|
S. Momani, Analytic and approximate solutions of the space- and time-fractional telegraph equations, Appl. Math. Comput., 170 (2005), 1126-1134.
doi: 10.1016/j.amc.2005.01.009.
|
[24]
|
E. Orsingher and L. Beghin, Time-fractional telegraph equations and telegraph processes with brownian time, Probab. Theory Relat. Fields, 128 (2004), 141-160.
doi: 10.1007/s00440-003-0309-8.
|
[25]
|
A. Saadatmandi and M. Mohabbati, Numerical solution of fractional telegraph equation via the tau method, Math. Rep., 17 (2015), 155-166.
|
[26]
|
J. Sabatier, O. P. Agrawal and J. A. Tenreiro Machado (Editors), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, World Book Incorporated Beijing, 2014.
doi: 10.1007/978-1-4020-6042-7.
|
[27]
|
M. Stynes, E. O' Riordan and J. L. Gracia, Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation, SIAM J. Numer. Anal., 55 (2017), 1057-1079.
doi: 10.1137/16M1082329.
|
[28]
|
Z. Sun and G. Gao, Finite Difference Methods for Fractional Differential Equations, Science Press, Beijing, 2015.
|
[29]
|
V. V. Uchaikin, Fractional Derivatives for Physicists and Engineers: Volume II Applications, Higher Education Press; Springer, Heidelberg, Beijing, 2013.
doi: 10.1007/978-3-642-33911-0.
|
[30]
|
S. Vong, P. Lyu and Z. Wang, A compact difference scheme for fractional sub-diffusion equations with the spatially variable coefficient under neumann boundary conditions, J. Sci. Comput., 66 (2016), 725-739.
doi: 10.1007/s10915-015-0040-5.
|
[31]
|
H. Wang, A. Cheng and K. Wang, Fast finite volume methods for space-fractional diffusion equations, Discrete Contin. Dyn. Syst. Ser. B., 20 (2015), 1427-1441.
doi: 10.3934/dcdsb.2015.20.1427.
|
[32]
|
L. Wei, H. Dai, D. Zhang and Z. Si, Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation, Calcolo, 51 (2014), 175-192.
doi: 10.1007/s10092-013-0084-6.
|
[33]
|
P. Xanthoulos and G. E. Zouraris, A linearly implicit finite difference method for a Klein-Gordon-Schrödinger system modeling electron-ion plasma waves, Discrete Contin. Dyn. Syst. Ser. B., 10 (2008), 239-263.
doi: 10.3934/dcdsb.2008.10.239.
|
[34]
|
X. Yang, L. Wu, S. Sun and X. Zhang, A universal difference method for time-space fractional Black-Scholes equation, Adv. Differ. Equ., (2016), Paper No. 71, 14 pp.
doi: 10.1186/s13662-016-0792-8.
|
[35]
|
A. Yildirim, He's homtopy perturbation method for solving the space and time fractional telegraph equations, Int. J. Comput. Math., 87 (2010), 2998-3006.
doi: 10.1080/00207160902874653.
|
[36]
|
Z. Zhao and C. Li, Fractional difference/finite element approximations for the time-space fractional telegraph equation, Appl. Math. Comput., 219 (2012), 2975-2988.
doi: 10.1016/j.amc.2012.09.022.
|