Results of the diffusive logistic equation in H₀^, p

Abstract In the present article, we first introduce the problem of the diffusive logistic equation with memory in Bessel potential spaces, discussing the parameters and and, in particular, their influence on the memory term of the model. Next, we present a result via a lemma that provides an estimate for the integral of a Mittag-Leffler function in terms of the memory effect. Based on this, using the Banach Fixed Point Theorem, Gronwall’s inequality, and the lemma estimating the Mittag-Leffler function, we investigate the existence, uniqueness, regularity, and continuous dependence of weak solutions to the diffusive logistic equation.