Abstract
In this paper, we approximate the solution to time-fractional telegraph equation by two kinds of difference methods: the Grunwald formula and Caputo fractional difference.
Highlights
The classical telegraph equation has another name of the transmission line equation
Because it is originated from the variational relationship between the voltage wave and the current wave on the well-proportioned transmission line, such equation can describe the ordinary diffusion phenomena well
Cascaval [1] investigated several aspects of the fractional telegraph equation, in an effort to better understand the anomalous diffusion process observed in blood flow experiments
Summary
The classical telegraph equation has another name of the transmission line equation. Because it is originated from the variational relationship between the voltage wave and the current wave on the well-proportioned transmission line, such equation can describe the ordinary diffusion phenomena well. Zhao [2] used the Fourier transform methods to studied the space-fractional telegraph equation. W. Jiang [7] obtained the exact solution to the time-fractional telegraph equation with Robin boundary value conditions by using the reproducing kernel theorem. Momani [9] to achieve analytic and approximate solutions to the space and time fractional telegraph equation. Chen [10] solved a time-fractional telegraph equation with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann, Robin boundary conditions. Orsingher and Beghin [13] obtained the Fourier transform of the fundamental solutions to time-fractional telegraph equations of order 2α. Some authors have already studied the numerical solutions to some kinds of time or space fractional telegraph equations, such as C.
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