Monotonicity of Positive Solutions for Dual Fractional Parabolic Equation Involving Fully Nonlinear Nonlocal Operator

In this article, we investigate the monotonicity of positive solutions for fully nonlinear fractional order parabolic equations involving the fractional time derivative by applying the moving planes method. We first establish a series of key theorems in the proofs, such as narrow region principles and averaging effects. Then, we use these tools to demonstrate the monotonicity of positive solutions in a half‐space.