An analytical solution of the time-fractional telegraph equation describing neutron transport in a nuclear reactor

Fractional telegraph equation is introduced to promote a sub-diffusive transport model of the neutrons inside a nuclear reactor. Here, the time derivatives of the classical telegraph equation have been replaced by the Caputo fractional derivative. In this paper, the fractional solutions are obtained through a technique that relies heavily on Fourier and Laplace transformations and is given in terms of the M-Wright function. The neutron flux density is clarified for different values of the time-fractional order.