NEW RESULTS FOR PARABOLIC EQUATION ON THE SPHERE WITH CAPUTO–FABRIZIO OPERATOR.

In this paper, we are interested in studying the initial value problem for parabolic problem associated with the Caputo–Fabrizio derivative. We deal the problem in two cases: linear inhomogeneous case and nonlinearity source term. For the linear case, we derive the convergence result of the mild solution when the fractional order α → 1 − under some various assumptions on the initial datum. For the nonlinear problem, we show the existence and uniqueness of the mild solution using Banach fixed point theory. We also prove the convergence result of the mild solution when the fractional order α → 1 − . [ABSTRACT FROM AUTHOR]