Fuzzy fractional differential equations with interactive derivative

Abstract

In this manuscript we present the concept of fuzzy fractional differential equation considering the fuzzy relationship of interactivity. We develop the theory of integral equation and fractional differentiability from the point of view of interactivity, that is, the fuzzy Caputo fractional derivative is given by fuzzy interactive derivative. We propose the fractional initial value problem via the interactive fuzzy Caputo fractional derivative and we comment on the usefulness of the interactive fuzzy derivative in the fractional context, since there are two fuzzy processes involved. Finally, we apply the results in two models of population dynamics, namely the Malthusian model and the Verhulst model, where analytical and numerical solutions are presented.