On well-posedness of the sub-diffusion equation with conformable derivative model

Authors: Nguyễn Huy Tuấn, Tran Bao Ngoc, Donal O'Regan, Dumitru Baleanu, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.1016/j.cnsns.2020.105332

Publisher, magazine: ,

Publication year: 2020

  Lưu        Trích dẫn         Chia sẻ

Abstract

In this paper, we study an initial value problem for the time diffusion equation on Ω × (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: • i.e., linear source term; • is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. • is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as – Time Ginzburg-Landau equations ; – Time Burgers equations ; etc.

Tags: Conformable derivative ,Nonlocally differential operator, Diffusion equation, Existence and regularity, Ginzburg-Landau equation, Burger equation