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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.

65M70Spectral, collocation and related methods (IVP of PDE)
35L20Second order hyperbolic equations, boundary value problems
35R11Fractional partial differential equations
Full Text: DOI
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