Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere

Abstract

Pseudo-parabolic equation on spheres have many important applications in physical phenomena, oceanography and meteorology, geophysics. The main purpose of this paper is to prove the existence and unique solution of the nonlinear pseudo-parabolic equation on the sphere. To do this, we used some analysis of Fourier series associated with several evaluations of the spherical harmonics function. Some of the upper and lower bounds of the Mittag-Lefler functions are also used. This result is one of the first studies of fractional nonclassical diffusion equation on the sphere.