The paper discusses the solution of a simple kinetic equation of the type used for the computation of the change of the chemical composition in stars like the sun. Starting from the standard form of the kinetic equation it is generalized to a fractional kinetic equation and its solutions in terms of H -functions are obtained. The role of thermonuclear functions, which are also represented in terms of H- and H - functions. In such a fractional kinetic equation is emphasized. Results contained in this paper are related to recent investigations of possible astrophysical solutions of the solar neutrino problem.