Fractional stochastic partial differential equation for random tangent fields on the sphere

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of random tangent vector field on unit sphere. The SPDE is governed by diffusion operator Lévy-type behaviour spatial solution, derivative in time depict intermittency its temporal and driven vector-valued Brownian motion sphere characterize long-range dependence. solution presented form Karhunen–Loève expansion terms spherical harmonics. Its covariance matrix function established as tensor that an Legendre kernels. variance increments approximations solutions are studied convergence rates approximation errors given. It demonstrated how these depend decay power spectrum variances motion.