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**An approximate analytical solution of time-fractional telegraph equation.**
*(English)*
Zbl 1216.65135

Summary: The powerful, easy-to-use and effective approximate analytical mathematical tool homotopy analysis method is used to solve the telegraph equation with fractional time derivative \(\alpha\) \((1 < \alpha \leqslant 2\)). By using initial values, explicit solutions of the telegraph equation for different particular cases are derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical model.

### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35L20 | Initial-boundary value problems for second-order hyperbolic equations |

35R11 | Fractional partial differential equations |

### Keywords:

telegraph equation; fractional time derivative; fractional Brownian motion; homotopy analysis method; numerical examples
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\textit{S. Das} et al., Appl. Math. Comput. 217, No. 18, 7405--7411 (2011; Zbl 1216.65135)

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### References:

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