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.


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
Full Text: DOI


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