Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport

•The time-fractional telegraph model as a useful description of the neutron transport process is generated.•A new hybrid scheme based LRBF-FD method is formulated to approximate the time-fractional telegraph model.•The LRBF-FD method useful for complex domains with acceptable accuracy was proposed.•The stability and convergence are examined using the energy method. This paper focusses on the numerical solution of the nonlinear time-fractional telegraph equation formulated in the Caputo sense. This model is a useful description of the neutron transport process inside the core of a nuclear reactor. The proposed method approximates the unknown solution with the help of two main stages. At a first stage, a semi-discrete algorithm is obtained by means of a difference approach with the accuracy O(τ3−β), where 1