Stability/Instability Maps Of The Neutron Point Kinetic Model With Conformable And Caputo Derivatives

Behavior analysis of the neutron point kinetic model with Caputo and conformable derivatives (Khalil and Almeida operators) was performed. Hence, boundary thresholds that delimit the stability/instability zones within the anomalous diffusion exponent-reactivity parameter space were found. Stability criteria are established to limit the region of the values of the anomalous diffusion coefficient and reactivity parameters with which the oscillatory behavior of the neutron density does not exceed a value greater than 30% with respect to the value of the classical model. The parameter space map corresponding to the model with Caputo derivative shows a larger stability behavior zone than that obtained with the Khalil derivative defined in terms of a linear kernel. In a more general sense, the Almeida operator allows one to freely define the kernel function. A kernel of exponential type produces instabilities of different nature (significant increase in neutron density followed by a series of decreasing oscillations few moments after the start-up, or a rapid growth in neutron density resembling a Gaussian pulse appearing seconds after the start-up), as well as stability/instability zones of different shapes and sizes as the parameters in the kernel vary. Interestingly, it was possible to reduce the instability behavior zone with the exponential kernel and approximate its size with that of the zone predicted with the Caputo derivative.