Existence of solutions to a fractional differential equation in the Heisenberg group

Abstract:

In this article, we start by performing a simple conversion of equation (1) to equation (2), then Liouville-type theorem is described afterward. We take in consideration the well-known high order semi linear parabolic equations with a non-linear infinite memory term. In third part of this article, we review the elements in which we prove the local existence of such equations with an infinite memory of nonlinear terms.