Abstract
The solution of a general time fractional wave equation for a vibrating string is obtained in terms of the Mittag–Leffler-type functions and complete set of eigenfunctions of the Sturm–Liouville problem. The time fractional derivative used is taken in the Caputo sense, and the method of separation of variables and the Laplace transform method are used to solve the equation. Some results for special cases of the initial and boundary conditions are obtained and it is shown that the corresponding solutions of the integer order equations are special cases of those of time fractional equations. The proposed general equation may be used for modeling different processes in complex or viscoelastic media, disordered materials, etc.
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