We extend the classical nonlinear space-dependent reactor kinetics analysis of Kastenberg and Chambré to incorporate fractional derivatives in both time and space. The neutron flux and temperature are governed by fractional partial differential equations: a Caputo time derivative of order α ∈ (0, 1] and a spectral fractional Laplacian of order β ∈ (0, 2]. Using a comparison principle for fractional parabolic operators, proved here via the positivity of the fractional heat semigroup, we prove asymptotic stability of equilibrium states for the prompt feedback and adiabatic models. The stability criteria are expressed in terms of the generalized buckling κ02 and the principal eigenvalue λ1(β) of the fractional Laplacian. For the prompt feedback model, the zero solution is asymptotically stable when κ02≤λ1(β), while a positive steady state is stable when κ02>λ1(β). For the adiabatic model, the temperature converges to a positive steady state. Simple comparison functions using Mittag–Leffler eigenfunction expansions provide explicit error bounds. Finally, we analyse a spectral Galerkin–L1 discretisation. We prove that it satisfies a discrete comparison principle, so that the numerical solution inherits positivity and the Mittag–Leffler bounds. We also derive its convergence rates on uniform and graded meshes and confirm them numerically.
