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

Guan Tingting, Wang Guotao, Araci Serkan

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240031

This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère 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-Ampère 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-Ampère equations.