General analytical solution of fractional Klein–Gordon equation in a spherical domain

 Fetecau, Constantin and Vieru, Dumitru

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Time-fractional Klein–Gordon equation in a sphere is considered for the case of central symmetry under the time-variable Dirichlet condition. The time-fractional derivative with the power-law kernel is used. The Laplace transform and convenient transformations of the independent variable and unknown function are used to determine the general analytical solution of the problem in the Laplace domain. In order to obtain the solution in the real domain, the inverse Laplace transforms of two functions of exponential type whose expressions are new in the literature have been determined. The similar solution for ordinary Klein–Gordon equation is a limiting case of general solution but a simpler form for this solution is provided. The convergence of general solution to the ordinary solution and the effects of fractional parameter on this solution are graphically underlined.

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 Fetecau, Constantin,  Vieru, Dumitru