On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term - Binh Duy Ho; Van Kim Ho Thi; Long Le Dinh; Nguyen Hoang Luc; Phuong Nguyen (Advances in Mathematical Physics)
In this paper, we examine a nonlinear fractional diffusion equation containing viscosity terms with derivative in the sense of Caputo-Fabrizio. First, we establish the local existence and uniqueness of lightweight solutions under some assumptions about the input data. Then, we get the global solution using some new techniques. Our main idea is to combine theories of Banach’s fixed point theorem, Hilbert scale theory of space, and some Sobolev embedding.