## 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
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### References:

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