Notes on continuity result for conformable diffusion equation on the sphere: The linear case

Abstract

In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order. The main technique is based on several evaluations on the sphere using spherical basis functions. To overcome the difficulty, we also need to use some calculations to control the generalized integrals.

Keywords

• parabolic equation
• conformable derivative
• sphere
• spherical harmonic
• 35r11
• 35b65
• 26a33