A Fractional Differential Equation Model and Dynamic Analysis of Animal Avoidance Learning

This article employs a fractional differential equation model to probe the dynamic mechanism of animal avoidance learning and memory retention. This model encompasses both linear and nonlinear scenarios. We first obtain the series-type analytical solution for the linear scenario and its absolute uniform convergence by Laplace transform and Mittag–Leffler function. Secondly, we establish the existence, uniqueness and Ulam–Hyers stability for the nonlinear scenario via the fixed point theorem and analytical techniques. Eventually, some examples and numerical simulations are provided to examine the effectiveness and availability of the main findings.