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Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space. (English) Zbl 1223.35112
Summary: The reproducing kernel theorem is used to solve the time-fractional telegraph equation with Robin boundary conditions. The time-fractional derivative is considered in the Caputo sense. We discuss and derive the exact solution in the form of series with easily computable terms in the reproducing kernel space.
MSC:
35C20Asymptotic expansions of solutions of PDE
35L20Second order hyperbolic equations, boundary value problems
35R11Fractional partial differential equations
References:
[1]Chen, Chang-Ming; Liu, F.; Turner, I.; Anh, V.: A Fourier method for the fractional diffusion equation describing sub-diffusion, J comput phys 227, 886-897 (2007) · Zbl 1165.65053 · doi:10.1016/j.jcp.2007.05.012
[2]Chen, Chang-Ming; Liu, F.; Burrage, K.: Finite difference methods and a Fourier analysis for the fractional reaction – subdiffusion equation, Appl math comput 198, 754-769 (2008) · Zbl 1144.65057 · doi:10.1016/j.amc.2007.09.020
[3]Liu, F.; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K.: Stability and convergence of difference methods for the space – time fractional advection – diffusion equation, Appl math comput 191, 12-20 (2007) · Zbl 1193.76093 · doi:10.1016/j.amc.2006.08.162
[4]Zhang, P.; Liu, F.: Implicit difference approximation for the time fractional diffusion equation, J appl math comput 22, No. 3, 87-99 (2006) · Zbl 1140.65094 · doi:10.1007/BF02832039
[5]Liu, Q.; Liu, F.; Turner, I.; Anh, V.: Approximation of Lévy – Feller advection – dispersion process by random walk and finite difference method, J comput phys 222, 57-70 (2007) · Zbl 1112.65006 · doi:10.1016/j.jcp.2006.06.005
[6]Yuste, S. B.; Acedo, L.: An explicit finite difference method and a new von neumman-type stability analysis for fractional diffusion equations, SIAM J numer anal 42, No. 5, 1862-1874 (2005) · Zbl 1119.65379 · doi:10.1137/030602666
[7]Benson, D. A.; Wheatcraft, S. W.; Meerschaert, M. M.: Application of a fractional advection – dispersion equation, Water resour res 36, No. 6, 1403-1412 (2000)
[8]Benson, D. A.; Wheatcraft, S. W.; Meerschaert, M. M.: The fractional-order governing equation of Lévy motion, Water resour res 36, No. 6, 1413-1423 (2000)
[9]So, F.; Liu, K. L.: A study of the subdiffusive fractional Fokker – plank equation of bistable systems, Physica A 331, 378-390 (2004)
[10]Me1zler, R.; Klafter, J.: The random walks guide to anomalous diffusion: a fractional dynamics approach, Phys rep 339, 1-77 (2000) · Zbl 0984.82032 · doi:10.1016/S0370-1573(00)00070-3
[11]Tan, Wenchang; Fu, Chaoqi; Fu, Ceji; Xie, Wenjun; Cheng, Heping: Subdiffusion model for calcium spark in cardiac myocytes, Appl phys lett 91, 183901 (2007)
[12]Eckstein, E. C.; Goldstein, J. A.; Leggas, M.: The mathematics of suspensions: Kac walks and asymptotic analyticity, Electron J differ eqs 3, 39-50 (1999) · Zbl 0963.76090 · doi:emis:journals/EJDE/conf-proc/03/e1/abstr.html
[13]Eckstein, E. C.; Leggas, M.; Ma, B.; Goldstein, J. A.: Linking theory and measurements of tracer particle position in suspension flows, Proc ASME FEDSM 251, 1-8 (2000)
[14]Orsingher, E.; Beghin, L.: Time-fractional telegraph equation and telegraph processes with Brownian time, Probab theory related fields 128, 141-160 (2004) · Zbl 1049.60062 · doi:10.1007/s00440-003-0309-8
[15]Beghin, L.; Orsingher, E.: The telegraph process stopped at stable-distributed times connection with the fractional telegraph equation, Fract calc appl anal 6, 187-204 (2003) · Zbl 1083.60039
[16]Chen, J.; Liu, F.; Anh, V.: Analytical solution for the time-fractional telegraph equation by the method of separating variables, J math anal appl 338, 1364-1377 (2008) · Zbl 1138.35373 · doi:10.1016/j.jmaa.2007.06.023
[17]Momani, S.: Analytic and approximate solutions of the space- and time-fractional telegraph equations, Appl math comput 170, 1126-1134 (2005) · Zbl 1103.65335 · doi:10.1016/j.amc.2005.01.009
[18]Podlubny, I.: Fractional differential equations, (1999)
[19]Cui, Minggen; Lin, Yingzhen: Nonlinear numerical analysis in the reproducing kernel space, (2009)
[20]Liu, F.; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K.: Stability and convergence of the difference methods for the space – time fractional advection – diffusion equation, Appl math comput 191, 12-20 (2007) · Zbl 1193.76093 · doi:10.1016/j.amc.2006.08.162