PDEs on spheres have many important applications in physical phenomena, oceanography, and meteorology, geophysics. In this paper, we study parabolic systems with the Caputo–Fabrizio derivative. In order to establish the existence of the mild solution, we use the Banach fixed point theorem and some analysis of Fourier series associated with several evaluations of the spherical harmonics function. Some of the techniques on upper and lower bounds of the Mittag–Leffler functions are also applied. This is one of the first research results on the systems of parabolic diffusion on the sphere.