Some applications and maximum principles for multi-term time-space fractional parabolic Monge-Ampère equation

Abstract

This study first establishes several maximum and minimum principles involving the nonlocal Monge-Amp & egrave;re operator and the multi-term time-space fractional Caputo-Fabrizio derivative. Based on the maximum principle established above, on the one hand, we show that a family of multi-term time-space fractional parabolic Monge-Amp & egrave;re equations has at most one solution; on the other hand, we establish some comparison principles of linear and nonlinear multi-term time-space fractional parabolic Monge-Amp & egrave;re equations.